I've noticed that 解ける which means 'to be solved' and 溶ける, 'to dissolve' are pronounced the same way. Furthermore the second one can be written using the kanji of the first one. That relation between both words is really similar to the one between the English word solve / dissolve, which made me ask that question: was the use of the words 解ける / 溶ける influenced by the English language? (e.g. solve a mystery as a metaphor coming from dissolving a chemical)
I think the pair 解ける 溶ける was probably not influenced by the English language.
Rather, it is more likely a standard example of the very common phenomenon of a (native Japanese) verb being written with different kanji to differentiate between various nuances/meanings. There are many, many such verbs
みる → 見る "to see", 観る "to watch", 看る "to look after", 診る "to examine"
きく → 聞く "to hear", 聴く "to listen", 効く "to have an effect", 利く "to function"
(Monolingual dictionaries will list these as 同源 "same origin".)
Of course you're correct in observing that this phenomenon is similar to the one of a verb like solve taking (in this case) a prefix to convey a more nuanced meaning, such as dissolve, resolve, absolve. But of course, correlation does not imply causation.