Problem: The sum of digits of two digit number is 8 and difference between the numbers and that formed by reversing the digit is 18. Find the number?

Step 1: Understanding the problem
To solve the problem, we need to find a two-digit number with the given conditions. The two conditions are:
- The sum of digits of the number is 8
- The difference between the number and the number formed by reversing the digits is 18.

Step 2: Using algebraic equations
Let's assume the two-digit number as '10a+b', where 'a' and 'b' are the digits of the number. We know that the sum of digits is 8, which means a+b=8.

Now, we need to find the difference between the number and the number formed by reversing the digits. If we reverse the digits of the number, we get '10b+a'. The difference between the number and the number formed by reversing the digits is (10a+b) - (10b+a) = 9a - 9b = 9(a-b). We know that this difference is 18. So, we can write the equation as:

9(a-b) = 18

Simplifying the equation, we get:

a - b = 2

We have two equations now:
a + b = 8
a - b = 2

We can solve these equations to find the values of 'a' and 'b'.

Step 3: Solving the equations
Adding the two equations, we get:

2a = 10

a = 5

Substituting the value of 'a' in the first equation, we get:

5 + b = 8

b = 3

So, the two-digit number is 53.

Step 4: Verification
Let's verify if the number satisfies both the conditions.
- The sum of digits is 5+3=8, which is correct.
- The difference between the number and the number formed by reversing the digits is (53 - 35) = 18, which is also correct.

So, the answer is 53.