Do I need to write exactly what is on my 1098T or do I use the supplemental information that helps calculate what has actually been paid?

No, you do not need to enter exactly what the Form 1098-T says.  You are allowed to adjust the actual tuition fees you paid out of pocket in box 2. 

On the replica of Form 1098-T screen, click on the blue link that says "what if this is not what I paid to this school?" (below box 2) to enter the full amount of tuition you actually paid.