Tal - simple number: one, two, six hundred and forty-five.
Antal - something you count: one apple, sixteen girls, twenty years.
Nummer - an assigned number: telephone number, prisoner number, house number. 'Nummer' also doesn't necessarily only consist of numbers. You could say "Det er prøve nummer 21A-5." - "That is sample number 21A-5."
But if RyagonIV is correct, and "tal" is a simple digit, then you are implying that "antal" is a sum i.e. the result of counting the number of things or the result of adding two numbers together. Therefore, "What is the total sum" should be accepted as correct (even though we do not say it in English, since "What is the TOTAL" obviates the need to use number/sum...