**Problem Statement:**
The sum of the digits of a two-digit number is 10. If 18 is subtracted from it, the resulting number will have equal digits. Find the original number.

**Solution:**

To solve this problem, we can break it down into the following steps:

1. Let's assume the two-digit number as "10x + y" where x and y are the digits.
- The tens digit is represented by x.
- The units digit is represented by y.

2. The sum of the digits is given as 10, so we can write an equation as:
- x + y = 10

3. We need to subtract 18 from the original number, so the resulting number will be:
- (10x + y) - 18

4. According to the problem, the resulting number will have equal digits.
- This means that the tens and units digits of the resulting number should be the same.
- So, we can write another equation as:
- x = y

5. Now, let's substitute the value of x from the second equation into the first equation:
- y + y = 10
- 2y = 10
- y = 5

6. Since x = y, we can conclude that x = 5 as well.

7. Now, we know that x = 5 and y = 5, so we can find the original number by substituting these values into the expression "10x + y":
- Original number = 10(5) + 5 = 55

8. Therefore, the original number is 55.

**Answer:**
The original number is 55.