Okay, let's tackle this math problem. We're starting with 77782 and subtracting 36037.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 2 in column 1 and get -5.
We add -5 to 10 and get 5 as the first digit of the result.

Step 2: We'll start by subtracting the digit 3 and the borrow 1 from 8 in column 2 and get 4.
4 is the next digit of our result.

Step 3: We'll start by subtracting the digit 0 and the borrow 0 from 7 in column 3 and get 7.
7 is the next digit of our result.

Step 4: We'll start by subtracting the digit 6 and the borrow 0 from 7 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 7 in column 5 and get 4.
4 is the next digit of our result.

So, 77782 - 36037 = 41745.