The reason why people tend to use the words "solve" and "resolve" interchangeably is that they are almost the same when you check their spellings. However, one of the major differences between the two is that they are not totally similar in terms of meaning, plus they can't be used in the same context to convey the same information.
One of the areas where you find people using the word "solve" the most is when they are trying to find a solution to a particular problem, at least this is very common in subjects like mathematics, and other related subjects. So, it won't make any sense trying to replace the word "solve" with "resolve" in this instance.
Another difference is that the word "solve" is a verb with several meanings, while the word "resolve" is both a noun and a verb. As a verb, it can be used to settle differences between two or more parties. It also means to make a firm decision to do something. As a noun, it means determination or the act of resolving something.