We can solve this together! We're beginning with 999776199 and removing 629672781 from it.

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

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

Step 3: We'll start by subtracting the digit 7 and the borrow 0 from 1 in column 3 and get -6.
We add -6 to 10 and get 4 as the next digit of the result.

Step 4: We'll start by subtracting the digit 2 and the borrow 1 from 6 in column 4 and get 3.
3 is the next digit of our result.

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

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

Step 7: We'll start by subtracting the digit 9 and the borrow 0 from 9 in column 7 and get 0.
0 is the next digit of our result.

Step 8: We'll start by subtracting the digit 2 and the borrow 0 from 9 in column 8 and get 7.
7 is the next digit of our result.

Step 9: We'll start by subtracting the digit 6 and the borrow 0 from 9 in column 9 and get 3.
3 is the next digit of our result.

So, 999776199 - 629672781 = 370103418.