What's the difference between 'resolve' and 'solve'?
First of all, resolve has several meanings. There is one meaning that is clearly closest to solve, which I will assume is the one you want to differentiate.
So: When you resolve something (a problem, an issue, a question), you deal with it conclusively. You have finished it, it is done, there is nothing left to concern yourself about. This is not to say, however, that your handling of the matter was ideal, nor even necessarily satisfactory; there are many possible ways that the thing could have been dealt with, you picked one and saw it through.
When you solve something, you find (and presumably implement) a solution to it. This means that you have dealt with it successfully, finding what was quite possibly the only way (or at most one of a few ways) to succeed.
Resolve is used to mean the end of a conflict--"The differences between the two parties were resolved."
Solve is used to mean the solution to a logical problem--"He solved the math puzzle."