57 is the number. 57+18=75. When we reverse 57 it comes 75 so 57 is the two digit number.

Problem:
The sum of the digits of a 2-digit number is 12. If 18 is added to it, the digits are reversed. Find the number.

Solution:
To solve this problem, let's break it down into steps.

Step 1: Understand the Problem
We are given a 2-digit number whose digits add up to 12. When we add 18 to this number, the digits are reversed. We need to find the original number.

Step 2: Represent the Problem Mathematically
Let's assume that the tens digit of the number is 'x' and the ones digit is 'y'. We can represent the original number as 10x + y and the reversed number as 10y + x.

Step 3: Form Equations
According to the given conditions:
- The sum of the digits is 12, so we can write the equation x + y = 12.
- When 18 is added to the original number, the digits are reversed, so we can write the equation 10x + y + 18 = 10y + x.

Step 4: Solve the Equations
We have two equations:
1) x + y = 12
2) 10x + y + 18 = 10y + x

Simplifying equation 2, we get:
9x - 9y = -18
Dividing both sides by 9, we get:
x - y = -2

Now we have a system of equations:
x + y = 12
x - y = -2

Adding these two equations, we eliminate 'y' and solve for 'x':
2x = 10
x = 5

Substituting the value of 'x' in equation 1, we can find 'y':
5 + y = 12
y = 7

Step 5: Verify the Solution
We have found that x = 5 and y = 7. So the original number is 57.
When we add 18 to 57, we get 75, which is the reversed number.

Conclusion:
The original number is 57.