The credit card company will issue a 1099C for the amount written off.
This is taxed as ordinary income.
So for example, if you were in the 15% tax bracket for 2016, and income is expected to stay close to same, then the amount written off would be taxed at 15% (so $10,000 would be $1,500 tax).
The tax brackets are listed below and may help you in determining what tax bracket you are in.
https://www.irs.com/articles/2016-federal-tax-rates-personal-exemptions-and-standard-deductions
