That's a math problem in fact, not solely programming.

that's why programmers have to learn maths anyways

No negative number can be solution to this.
abs(a-b) is non-negative, so c is positive (c>0).
If a if negative:

• if a ≥ b, then b is negative too, and abs(a-b) < c turns into a-b < c => 0 < c < a+b < 0 => False;
• if a < b, then abs(a-b) < c => b-a < c < b+a; but with a < 0, b-a > b+a.
  So, our proposition of negative a leads to contradiction. And because a and b are symmetric in this expression, this also is true for negative b.
  Zeros are eliminated by using strict ineqaulities.
  Thus, only positive values of a,b and c conforms this expression.

You may not consider the negative cases