Alright, let's solve this problem step by step. We have 582736 and 37977, and we're subtracting the second number from the first.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 6 in column 1 and get -1.
We add -1 to 10 and get 9 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 3 in column 2 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 3: We'll start by subtracting the digit 9 and the borrow 1 from 7 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 7 and the borrow 1 from 2 in column 4 and get -6.
We add -6 to 10 and get 4 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.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 5 in column 6 and get 5.
5 is the next digit of our result.

So, 582736 - 37977 = 544759.