Let the number will be 10x+y
So
sum of digits = 9
x + y = 9
x = 9-y
if digits are reversed, the new number will be 10y+x
And according to the question
(10x+y) - 9 = 10y+x
10x + y - 9 - 10y - x = 0
10x - x + y - 10y - 9 = 0
9x - 9y - 9 = 0
9(x - y - 1) = 0
x - y - 1 = 0 (use x = 9-y)
9 - y - y - 1 = 0
-2y + 8 = 0
2y = 8
y = 4
x = 9-y = 9-4 = 5
The number is 10x+y = 10×5+4 = 54