This is very interesting math word problem, which could be solved by applying simple quantitative reasoning rather than going deep into equation solving. The logic is as following.
In order to satisfy the first condition ("decreased by 72 when digits swap"), the first digit could be only 9 or 8 to get the positive number or null after subtracting 72. Number 9 is not acceptable because it will fail the second condition "sum of digits equal 8" (it exceeds 8 regardless of second digit).
Thus the only choice is 8 as the first digits leading to only one acceptable option of "0" as the second digit.
Number 80 satisfies both conditions; it is the answer.