The sum of the digits of a two-digit number is 10. When the digits are reversed, the number decreases by 36. Find the original number

We have a 2-digit number where the sum of the digits is 10. If we then take the 2-digit number and subtract 36 we get the 2-digit number, reversed.

The 2-digit number can be represented as 10a + b. And we know a + b = 10. We also know that 10a + b - 36 = 10b + a. Arranging gives us 9a - 9b = 36. And then divide by 9 gives us a - b = 4. Now we have a + b = 10 and a - b = 4. Adding those together gives us 2a = 14 and then a = 7. Following that b is 3. This means that the 2 digit number we’re looking for is 73.