Solve implies that there is a problem or a puzzle (or a puzzle-like problem) which you are trying to work out. When you solve the problem or puzzle, you have found its solution, which is the noun derived from the verb 'to solve.' 'Solve' and 'solution' both emphasize that the problem or puzzle has been completed, but also may suggest (to my mind, anyway) some ambiguity in either that it is only one way of solving the problem, or that the solution may not be permanent, or that the solution is hypothetical and has not yet been applied to the problem. Because puzzles usually have only one solution, we usually use 'solve' when talking about them; the ambiguities arise more with problems in real life or in more complex thinking. ..................................................................................................................... To resolve, when used in relation to a problem, addresses the ambiguity of 'solve.' When something is 'resolved' or there is a 'resolution', it emphasizes that the problem has been permanently (or at least durably) solved. We often talk about a resolution to conflict, which means that an answer has been reached that all parties involved are happy with, and the conflict has ended. We usually talk about solutions to the Israel-Palestine conflict because it's a complex situation with no obvious solution, and because the solutions that have been proposed are often theoretical and/or have not been applied to the situation and/or have not been long-lasting solutions.

To resolve is used differently than solve. To resolve is used when there are (usually) two differing opinions and there needs to be a decision made between the two. Resolve is used mainly with an argument between two people. Resolve is also used as a noun. "He has a lot of resolve", meaning: you have a lot of determination or you have the ability to put your mind to something deliberately. To solve a problem means to find an answer using all the information provided and determining the answer. To solve the crime, the police used all the evidence they found in the apartment. While solve has only limited meanings, resolve has much more meanings. see the following : Solve has the following meanings : 1. to find the answer or explanation for; clear up; explain: to solve the mystery of the missing books. 2. to work out the answer or solution to (a mathematical problem). Resolve has the following meanings : 1. to come to a definite or earnest decision about; determine (to do something): I have resolved that I shall live to the full. 2. to separate into constituent or elementary parts; break up; cause or disintegrate (usually followed by into ). 3. to reduce or convert by, or as by, breaking up or disintegration (usually followed by to or into ). 4. to convert or transform by any process (often used reflexively). 5. to reduce by mental analysis (often followed by into ). 6. to settle, determine, or state formally in a vote or resolution, as of a deliberative assembly. 7. to deal with (a question, a matter of uncertainty, etc.) conclusively; settle; solve: to resolve the question before the board. 8. to clear away or dispel (doubts, fears, etc.); answer: to resolve any doubts we may have had. 9.to come to a determination; make up one's mind; determine (often followed by on or upon ): to resolve on a plan of action. 10. to break up or disintegrate. 11. to be reduced or changed by breaking up or otherwise (usually followed by to or into ).