Okay, let's tackle this math problem. We're starting with 700199 and subtracting 40558.

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

Step 2: We'll start by subtracting the digit 5 and the borrow 0 from 9 in column 2 and get 4.
4 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 0 and the borrow 1 from 0 in column 4 and get -1.
We add -1 to 10 and get 9 as the next digit of the result.

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

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

So, 700199 - 40558 = 659641.