Okay, we are tasked with adding 9099 and 1009. Let's begin!

Step 1: We'll start by adding the digits 9 & 9 in column 1 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 0 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 0 in column 3 and get 1.

Step 4: We'll start by adding the digits 9 & 1 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 9099 + 1009 = 10108.

