You are looking for numbers of the form $\binom{a}{2}+\binom{b}{2} = \binom{c}{2} < 100$ where $a,b,c$ are integers greater than one.

This can be written: $a(a-1)+b(b-1) = c(c-1) < 200$

This is known as a Diophantine Equation. There are methods to solving these, but the math is extremely complex, and in this instance would likely take more work than a simple guess and check method. In mathematics, you typically look for the method that requires the least computation. So,

Here is a list of all triangle numbers up to 100:

1,3,6,10,15,21,28,36,45,55,66,78,91

Checking sums, you find many answers that work (I don't see how 36+55=91 is any better than any of these):

3+3 = 6

6+15 = 21

10+45 = 55

15+21 = 36

21+45 = 66

36+55 = 91

If the question asked for the total to be as close to 100 as possible, then 36+55=91 would be the solution, but as you posed it, there seem to be six valid answers.