Groups; solution to quadratic.

I'm new to groups and trying to answer the following question.

Let G be any group. Show that the identity e is the unique solution of the equation

So how do I proceed?
A group, as far as my primitive understanding goes, is a set governed by a binary operation, producing local inbred offspring; then we have the given axioms: closure, associativity, identity and invertibility.

So we assume G is a group with a binary operation or is it ?

Then what?

we know
and

Does this help?

What is the best and most comprehensive text on groups that starts at the absolute beginning?

You know that elements in a group are always invertible, so what happens when you multiply the identity by .

As for texts in groups, Rotman's An Introduction to the theory of groups is very good in my opinion.

If we let the binary operation be and we know that then (given ) therefore

How do we show it is a unique solution?