A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are interchanged. The number is

Let the number be "XY" .
Given the sum of digits =  X + Y = 8.........Equation 1

This XY can be written as : XY = Y(1) + X(10) 

Upon adding 18 to XY we get :  {10(X) + Y + 18}

Now, it is given this particular number is "YX" i.e it should be equal to {X + 10(Y)}.
Hence, 10(X) + Y + 18 = X + 10(Y)
9X - 9Y = -18
X - Y = (-2)..........Equation 2

By solving both equations : X = 3 & Y = 5.

Therefore, the number is 35.