Let the two-digit number be 10x + y, where x and y are digits.
Sum of number and reversed number:
\[(10x + y) + (10y + x) = 99\]
\[11(x + y) = 99 ⇒ x + y = 9\]
Given the digits differ by 7:
\[|x - y| = 7\]
Case 1: x - y = 7
From x + y = 9, add both equations:
\[2x = 16 ⇒ x = 8, y = 1\]
Number is 81.
Case 2: y - x = 7
From x + y = 9, add:
\[2y = 16 ⇒ y = 8, x = 1\]
Number is 18.
Thus, possible numbers are 81 and 18, but choosing 81 as the answer.