We can solve this together! We're beginning with 90408 and removing 8588 from it.

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

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

Step 3: We'll start by subtracting the digit 5 and the borrow 1 from 4 in column 3 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 4: We'll start by subtracting the digit 8 and the borrow 1 from 0 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 0 and the borrow 1 from 9 in column 5 and get 8.
8 is the next digit of our result.

So, 90408 - 8588 = 81820.