These two adjectives come from the same root, and insoluble has one meaning which is the same as that of insolvable, but also another more fundamental meaning.
Both insoluble and insolvable can mean “not solvable,” as in a problem, mystery, or riddle:
The tricky professor gave his students insoluble/insolvable physics problems.
Poverty may be an insoluble/insolvable problem, but we must try.
This is the only meaning of insolvable, and the second meaning of insoluble.
The first meaning of insoluble is “not dissolvable”; to dissolve means to spread apart in water or liquid until it disappears—like salt in water—as opposed to oil, which is insoluble in water. The problem-solving meaning of soluble is a metaphor; solving a problem is like making the problem dissolve in water!