Let the digit in the number is xy

So number is 10x + y

Given, sum of the digits of a two-digit number is 9

=> x + y = 11 ..........................1

Again

     10y + x = 10x + y - 45

=> 10x + y - 10y - x = 45

=> 9x - 9y = 45

=> 9(x - y) = 45

=> x - y = 45/9

=> x - y = 5  ..................2

Add equation 1 and 2, we get

      x + y + x - y = 11 + 5

=> 2x = 16

=> x = 16/2

=> x = 8

Now, from equation 1, we get

=> 8 + y = 11

=> y = 11 - 8

=> y = 3

So the required number is 83