Alright, let's solve this problem step by step. We have 9113 and 9582 and we're adding them together.

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

Step 2: We'll start by adding the digits 1 & 8 in column 2 and get 9.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 6.

Step 4: We'll start by adding the digits 9 & 9 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 9113 + 9582 = 18695.

