Question

What are three numbers that have a sum of 35 if the greatest number is 14 more than the least number?

Answer 1

There are infinitely many answers.
Even restricting yourself to integers, you have:
2, 16, 17 or 5, 19, 11 or 18, 32, -15.

Answer 2

let smallest number be x
let the largest number be x+14
let the middle number be y , such that y > x

x + x+14 + y = 35
2x + y = 21

y = -2x + 21

There is an infinite number of such triplets

e.g.

5, 11, 19
4, 13, 18
6, 9, 20
4.532, 11.936 , 18.532
1, 19, 15 ---> reject that one, since it does not satisfy both conditions.
... etc