Let the one’s digit be ‘a’ and ten’s digit be ‘b’

Given, sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45.

⇒ a + b = 13 ----- (1) and,

10a + b – (10b + a) = 45

⇒ 9a – 9b = 45

⇒ a – b = 5 ---------- (2)

Adding (1) and (2)

⇒ 2a = 18

⇒ a = 9

Thus, b = 4

Number is 10b + a

⇒ Number = 49