We can solve this together! We're beginning with 81597 and removing 8816 from it.

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

Step 2: We'll start by subtracting the digit 1 and the borrow 0 from 9 in column 2 and get 8.
8 is the next digit of our result.

Step 3: We'll start by subtracting the digit 8 and the borrow 0 from 5 in column 3 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 4: We'll start by subtracting the digit 8 and the borrow 1 from 1 in column 4 and get -8.
We add -8 to 10 and get 2 as the next digit of the result.

Step 5: We'll start by subtracting the digit 0 and the borrow 1 from 8 in column 5 and get 7.
7 is the next digit of our result.

So, 81597 - 8816 = 72781.