That's right. 113=100+10+3 and 29=20+9.
So when we subtract we are actually doing: 100+10+3-20-9.
This can be arranged by grouping the numbers to make the subtraction easier:
(100-20)+(10+3-9)=80+13-9=80+4=84. Or 100-20+10-9+3=80+1+3=84.
So, the 10 has been removed from 113 and used in the subtraction because we can't subtract 9 from 3 in the ones position without help from the tens.
Here's another way of thinking about it.
Imagine a set of three drawers. In the top drawer we have the hundreds, the middle drawer the tens and the bottom drawer the ones. We replace the digits with blocks. In this case a block in the top two drawers and 3 in the bottom drawer. But these blocks are boxes. The top drawer box contains 10 smaller boxes which are the same size as the blocks in the middle drawer. And the middle drawer contains 10 even smaller boxes the size of those in the bottom drawer.
We come along and we want to take 29 away from what we have in the drawers. Let's start with the bottom drawer with just 3 boxes or blocks. We can't take away 9! So we go to the next drawer and take out the only box in it, leaving the middle drawer empty, and empty all the blocks in it into the bottom drawer so we now have 13 blocks and we can easily take away 9 leaving 4 blocks. Close the bottom drawer.
The middle drawer is empty! We need to take 2 blocks or boxes and there aren't any! So we take the box out of the top drawer and empty it into the middle drawer so we have 10 boxes in it. So we remove 2 leaving 8.
We are left with nothing in the top drawer, 8 blocks/boxes in the middle drawer and 4 in the bottom. That represents the number 84.