The integers are -8 and -6.
To find these, first assume that the first integer is x. Then, because it is an even integer, assume the next is x + 2. Now we can write an equation to solve.
Tripling the greater = subtracting 10 from the lesser
3(x + 2) = x - 10 ----> Distribute the 3
3x + 6 = x - 10 ----> Subtract x from both sides
2x + 6 = -10 ----> Subtract 6 from both sides
2x = -16 ----> Divide both sides by 2
x = -8
Which is the first integer. We then can determine that the second one, which is two higher than the first, would be -6.