loosely speaking they can be used in same situations.
Can be a matter of context and subjective taste.

You solve math/engineering/science problems

You resolve issues

solve has a sense of definitive resolution whereas resolve might imply no clear outcome but merely that there has been some compromise and the issue is no longer on the table for discussion.

You

resolve issues (like childhood trauma)
solve problems (like math)

but I bet immediatley there will be a million exceptions to this generalization.

Thanks a billion, that helps. :)