Basically, if you work through the program the way it's designed and intended to be used, you'll be entering mortgage interest for the rental first. Based upon your selections, the program (not you) will split that mortgage interest between SCH E based on the percentage of space that is rented and the time it was rented for the tax year, and SCH A for the percentage of space that is personal use, as well as the time is was personal use during the year.
Assuming you only have one single 1098 to deal with, the amount on line 8 of the SCH A and the amount on line 12 of the SCH E should add up to the total reported on the 1098.
If you are affected by SALT, then that only affects the amount on SCH A and not the amount on SCH E.