My soon to be ex wife will not give me her social security number

If you can't retrieve her social security number, you won't be able to e-file and will need to print and mail your return. Do you have a copy of a prior year return? You may be able to retrieve the information by viewing your records online if you have an account with the IRS. 

Are you filing married filing separately?   Interesting----since she needs your SSN in order to file MFS.   When you file MFS each of you has to enter information about their spouse because the IRS cross checks to make sure you are both following all of the strict rules for that filing status.   If you have an attorney you might need help from your attorney for this issue.

If you have filed a joint return in a past year, you could try getting a copy of a past return from the IRS-it would have the SSN's on the return.   Free transcripts only show four digits.

You can pay the IRS $43 for an actual copy of your tax return which will include copies of your W-2’s     

https://www.irs.gov/pub/irs-pdf/f4506.pdf