My daughter attends a foreign college. We paid $6286 in tuition but cannot deduct it because no 1098-T will be provided. I read we can deduct $4K with an explanation?

No. 

But you still may be able to deduct it. If so, in TT after answering no to the do you have a 109-T question, answer yes to the exception question.

 To be eligible for the tuition credits or tuition & fees deduction, the course must be taken at "an eligible institution". The school should be able to tell you if it is an eligible educational institution. In general, an eligible educational institution is an accredited college, university, vocational school, or other postsecondary educational institution, including accredited, public, nonprofit, and proprietary (privately-owned, profit-making) postsecondary institutions. Additionally, in order to be an eligible educational institution, the school must be eligible to participate in a student aid program administered by the Department of Education.  foriegn schools do not have to issue a 1098- T (exception)

Enter your school at the link below, to see if it's on the dept. of education list.

https://fafsa.ed.gov/FAFSA/app/schoolSearch?locale=en_EN (choose foreign country for state)