Let one of the numbers be n then the other must be 66-n since their sum is 66.
Let's see what 2n-(66-n)=177 gives us: 2n+n=177+66=243, so 3n=243, n=81, but that would mean that the other number is 66-81=-15. In this case we found the larger number first. 81+(-15)=81-15=66.
In this case, n was the larger number because all positive numbers are greater than negative numbers. The two numbers are 81 and -15.
But let's see what 2(66-n)-n=177 gives us: 132-3n=177, so 3n=132-177=-45, n=-15 and 66-n=66+15=81, giving us the same pair of numbers 81 and -15. In this case we found the smaller number first.