Sure you need  58^10  combinations, which is quite a lot. There is no other way that I see.
So you need a fast algorithm.
I could probably write something in Javascript or Python but they will not be fast enough I fear.

Is there no way to read one of the 10 missing characters even slightly ?
sometimes you can try to see where the paper is slightly pressed by the pen?
What kind of reward did you have in mind ?