En is a pronoun here. It refers to solution and in this way, one avoids in French weird turns like

Vous avez cherché une solution et vous avez trouvé une solution.

The correct turn is

Vous avez cherché une solution et vous en avez trouvé une. → You looked for a solution and you found one.

Note that en is always present, in correct French, for expressions of quantity, including numerals and indefinites; usually it is not conveyed in English.

Il en a pris une poignée. → He took a handful (of it).

J’en ai trouvé huit. → I found eight (of them).

Il n’en a pas d’autres. → He has not any others.

On en a perdu quelques-uns. → We have lost some.