To be perfectly honest, it's the words "essence" and "substance" that are problematic for me and many like me. I've yet to find anyone who can actually tell me what either of those two words really means. If you can do that, we might be able to make some headway.
Okay, I'm copying this from Anthony Flew, A
Dictionary of Philosophy, 1979. The copied portions are indented. I offer some commentary in non-indented paragraphs.
A term with several inter-related sense. 1. One definition of substance makes use of the logical notions of subject and predicate; regarded in this way, S is a substance if S is a subject of predicates, but cannot be predicated in turn of any other subject. This concept of substance can be traced back to Aristotle (Categories 2a12), and plays an important part in the philosophy of Leibnitz.
So, what's a predicate? It's the term that appears in the predicate position of a subject-predicate sentence; for example, 'man' in 'Socrates is a man.' It is that which is affirmed or denied of the subject. The same term can be a predicate of one sentence but a subject in another. For example, 'man' is the subject of 'Man is an animal.'
2. A substance of the kind just described is also said (for example, by Aristotle, Categories 2a13) to be that which does not exist in a subject, where something is understood to 'exist in' a subject if it cannot exist separately from it (Aristotle, Categories 1a24-5). In this sense, then, a substance may be said to be that which has an independent existence. Philosophers disagree about what has independent existence; for example, Aristotle said that a particular man is a substance, whereas Spinoza would say that only God has a truly independent existence....
3. One and the same substance (in senses 1 and 2) can have predicates that are contrary to each other, provided that these predicates are not simultaneous (compare Aristotle, Categories 4a10); that is, a substance which has the predicate P at one time may have the predicate not-P at another. Viewed in this way, a substance is regarded as that which remains the same through change. This concept of substance, which involves a reference to time, is defined by Kant in the Critique of Pure Reason.
4. The Greek word that is translated as 'substance' (ousia) can also be rendered as 'essence', and some philosophers view the substance of a thing as what it really is, as opposed to the way in which it appears. This sense of substance is related to sense 3, in that the essence is regarded as remaining the same, whereas the appearances change. Locke (who also uses the term 'substance' in sense 2) is among the philosophers who regard the substance of a thing as what it really is.
With this as background, what does "substance" and "essence" mean in the Christian creeds? I think the best senses for these words are 2 and 4. That is, Christians say that God is three persons, but those persons do not "divide the substance." We moderns might say there is one and only one divine "thing." When we say that the Father is God, the Son is God, and the Holy Spirit is God, we are not saying that there are three divine "things." Whatever "person" means, it doesn't mean "a thing separate from the divine being, God." So the persons don't "divide the substance."
All I know that if the Father is God, the Son is God, and the Holy Ghost is God, there are three individuals who are all "God."
Here you are using "God" as if it were some sort of title like "general" or "king." Christians don't use the word that way. They use the word "God" to denote a particular being.
As stated, your slogan is a restatement of tri-theism, the view that there are three gods. Christianity affirms that there is one and only one divine being, one and only one God. By "God", Christians have in mind a being that does not depend on anything else for its existence (sense 2 above). If your slogan were true, it would mean that there are three beings who each are self-sufficient, self-existing, relying on nothing else for their origin and continued existence. But Christians say that only one being relies on nothing else for its origin and continued existence -- the one and only God.
I mean something more like the word "team."
This gets exactly at the problem. This is exactly this meaning that the early Christians were at such pains to avoid. They wanted to fully uphold the traditional Jewish view of God as one and only one. God is in no sense a team. There are not a plurality of beings that share a title (like the San Antonio Spurs are a group of people, all equally human, who share the title "San Antonio Spur"). There is instead one and only one divine being (or, substance) which is undivided, not plural.
The unity or oneness of the Father, Son and Holy Ghost so far exceeds our comprehension that they can be thought of as "one God." Still, the Father is the Father. He is not also the Son. The Son is the Son. He is not also the Holy Ghost. The Holy Ghost is the Holy Ghost. He is not the Father.
Well, the unity you affirm is not as profound as that which the church proclaims. For the church says that the Father, Son, and Holy Spirit enjoy ontological unity. That is, there is only one divine being, which exists as three persons. So the persons share the same divine substance.
The trinitarian doctrine does not say that the Father is the Son or that the Son is the Holy Spirit or the Holy Spirit is the Father. It upholds BOTH the notion that there is only one divine substance/being/thing/item, AND that there are three "persons", each of whom are fully divine. The persons do not divide the substance (i.e., turn God into a team). Nor do the persons exist as independent beings in their own right.
I'm the first to admit that this is mysterious. Lots of ink has been spilled explicating this idea over the centuries. But it is understandable. After all, as far as I've explained it, I understand it. And I don't have extraordinary intelligence.