If there are attorneys involved, get your attorney to ask her attorney. Sharing SSNs when filing separate tax returns during separations is routine.
If not, you can't e-file. Print your return, sign it and mail it in. Attach a written statement giving your spouse's name, address, date of birth, and a brief explanation of why you don't have her SSN. You may need to make up a fake SSN to get Turbotax to print the return; if so, be sure to erase it or cover it with white-out before mailing your return.
