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.
The issue has been resolved, although none of us is happy with the final outcome.
The question has been solved; the correct answer is posted for all to see.
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."
I think that re-solution means that you need to separate two or more entities. Therefore,
resolution also stands for measurement quality: the stronger is your optics or sensors, the finer you can find the difference (between objects). Otherwise, if your resolution is too low, the objects look fused and you are confused. Confusion is opposite to resolution in the sense that you cannot separate the fused entities. Solution, on the other hand, means that you have only one task, one question and, if answer is found, you have solved it. You have nothing to distinguish between.