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?