To make things a little easier - unless you do a 1031 exchange (which you apparently have not since you got a check), realized and recognized will be the same amount.
You start by determining your adjusted basis - original cost + cost of improvements - accumulated depreciation = 10,000 + 90,000 - 10,000 = $90,000 adjusted basis.
Next you determine net selling price - stated sales price - commissions - other costs of selling (such as title insurance, attorney's fees, etc) = net selling price.
The difference between net selling price and adjusted basis is your realized (and recognized) gain.
The mortgage assumption does not really enter into the calculation except as a part of the "stated salesprice".
If your gain is $10,000 or less, it will be a Section 1250 gain and subject to a maximum tax rate of 25%. If the gain is more than $10,000, the first $10,000 will be Section 1250 (as above) and the balance will be Section 1231 gain which, in all likelihood, will wind up being taxed as a long term capital gain with a maximum tax rate of 15%.
Your actual rates of tax could be lower depending on your specific circumstances.