Let's get this math done. We have 81182 and 39518, and we're going to subtract the second number from the first.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 2 in column 1 and get -6.
We add -6 to 10 and get 4 as the first digit of the result.

Step 2: We'll start by subtracting the digit 1 and the borrow 1 from 8 in column 2 and get 6.
6 is the next digit of our result.

Step 3: We'll start by subtracting the digit 5 and the borrow 0 from 1 in column 3 and get -4.
We add -4 to 10 and get 6 as the next digit of the result.

Step 4: We'll start by subtracting the digit 9 and the borrow 1 from 1 in column 4 and get -9.
We add -9 to 10 and get 1 as the next digit of the result.

Step 5: We'll start by subtracting the digit 3 and the borrow 1 from 8 in column 5 and get 4.
4 is the next digit of our result.

So, 81182 - 39518 = 41664.