Let us assume that one of the digit of the two digit number is X, then problem the other number will be (8 - X)

From problem we get that, if we add 27 to the number the digits get interchanged and also since the number is a two digit number then X will in tens place (7 - X) will be in ones place.

So the equation we get

10X + (8 - X) + 18 = 10(8 - X) + X

10X + 8 - X + 18 = 80 -10X + X

9X + 26 = 80 - 9X

9X + 9X = 80 - 26

18X = 54

X = 54/18

X = 3,

So the digit in tens place = 3 the digit in ones place is (8 - 3 = 5) , then the number is 35 and when 18 is added the result is 53, the digits interchange their position in the new number.

**Ans: 35.**