Assume, the unit place digit will be y & the ten's place digit will be x
∴ The number will be 10x+y [Think it as, if the number is 13, then 10*1+3 = 13]
& the sum of the digits of the number will be x+y which is equal to 16 (already given)
x+y = 16 ----------- 1)
If the digits are reversed, the new number will be 10y+x
According to the question or the data given,
(10x+y) - (10y+x) = 18
10x + y - 10y -x = 18
Or, 9x - 9y = 18
Or, 9(x - y) = 18
Or, x - y = 18/9 = 2
Or, x - y = 2 ----------- 2)
Now, add 1) + 2)
x + y + x - y = 16 +2
Or, 2x = 18
Or, x = 9
Putting the value of x = 9 in equation 1)
x + y = 16
Or, 9 + y = 16
Or, y = 16 - 9 = 7
∴ The original number will be 97 & the reversed number is 79