The sum of the digits of a two digit number is 8 and the difference between the number and thatformed by reversing the digits is 18. Find the number.

Let's assume the two-digit number is represented as "10a + b", where 'a' represents the tens digit and 'b' represents the units digit.

According to the given information, the sum of the digits is 8. So, we can write the equation as:

a + b = 8 ----(1)

The difference between the number and the number formed by reversing the digits is 18. This can be written as:

(10a + b) - (10b + a) = 18 9a - 9b = 18 a - b = 2 ----(2)

Now, we have a system of equations (1) and (2) that we can solve simultaneously to find the values of 'a' and 'b'.

From equation (1), we can express 'a' in terms of 'b' as: a = 8 - b

Substituting this value of 'a' in equation (2), we get: (8 - b) - b = 2 8 - 2b = 2 -2b = -6 b = 3

Substituting the value of 'b' back into equation (1), we get: a + 3 = 8 a = 5

Therefore, the two-digit number is 53.