@rockpoppy,
rockpoppy wrote:
I am writing a letter and I have typed the following.
"Finding solutions to those challenges, I find extremely motivating."
Is this a sentence?
You have an inverted sentence pattern, with a subordinate clause followed by an independent clause with an elided phrase. To test for sentence completeness, you can put it back in standard order and reinstate the elision:
I find finding solutions to those challenges (to be) extremely motivating.
Good sentence. Run with it, I say.