How did you use that information to help solve/solving the problem?

Help licenses an infinitival (with or without to) as its complement.

The first version is grammatical, but the second, with a gerund-participial as the complement of help, is questionable.

In your case, solve the problem functions as the complement of help.

Your second sentence is not colloquial.

As it says in the Cambridge Dictionary:

We use help with or without an object:

Let me help you.
Can I help?

We also use help with an object and an infinitive with or without to:

Jack is helping me to tidy my CDs. or Jack is helping me tidy my CDs.

Thank you for helping us find the right hotel or thank you for helping us to find the right hotel.

Warning:

We don’t use help with an -ing form:

I am trying to help him look for a new bike.
Not:
I am trying to help him looking . . .

So you might say to help solve or to help to solve but not to help solving.