Okay, we are tasked with adding 8684498318 and 2281598138. Let's begin!

Step 1: We'll start by adding the digits 8 & 8 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 3 in column 2 and get 5.

Step 3: We'll start by adding the digits 3 & 1 in column 3 and get 4.

Step 4: We'll start by adding the digits 8 & 8 in column 4 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 5: We'll start by adding the digits 9 & 9 in column 5 and get 19.
We'll write down the last digit 9 and carry the 1 to the next column.

Step 6: We'll start by adding the digits 4 & 5 in column 6 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 7: We'll start by adding the digits 4 & 1 in column 7 and get 6.

Step 8: We'll start by adding the digits 8 & 8 in column 8 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 9: We'll start by adding the digits 6 & 2 in column 9 and get 9.

Step 10: We'll start by adding the digits 8 & 2 in column 10 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 8684498318 + 2281598138 = 10966096456.

