Box 1 on a 1098-T should report what was paid to (or received as payment by) the school in the calendar year. 

Box 1 is NOT used to report the difference between the scholarship and tuition costs. 

Check your records and adjust if necessary, but remember that school years and calendar years overlap. If tuition for 2018 was billed AND PAID FOR in 2017, that amount cannot be used. Only what was paid in 2018. Scholarships that post, and are not refunded to you, are considered as payments made by you. 

If you paid in 2018 and you feel that the amount is not properly included in Box 1, you can adjust the amount. Be sure you have source documents to prove that the payments were made in the tax year, such as the student's school account statement. Keep a copy of the statement with your tax file. Also, remember that you may need to adjust next year's 1098-T as well. 

Enter the 1098-T into the program as reported, but click the blue "What if this is not what I paid?" link under Box 1. On the page that opens (you may need to scroll down a bit) there is a space to enter what was paid to the school. 

According to the IRS:

“Generally, an eligible educational institution (such as a college or university) must send Form 1098-T (or acceptable substitute) to each enrolled student by January 31, 2019. An institution will report payments received (box 1) for qualified education expenses. However, the amount on Form 1098-T might be different from what you paid. When figuring the credit, use only the amounts you paid or are deemed to have paid in 2018 for qualified education expenses.”

CLICK HERE for IRS Pub 970 Tax Benefits for Education