Okay, so I need to compute 58 base 9 minus 18 base 9 and express the answer in base 9. Hmm, let's think about how to approach this. 

First, I remember that when subtracting numbers in a different base, the process is similar to base 10, but I have to be careful with the borrowing since the place values are powers of 9 instead of 10. Let me write down the numbers to visualize the subtraction:

```
  5 8
- 1 8
-------
```

Starting from the rightmost digit, which is the ones place in base 9. So, subtract 8 (base 9) from 8 (base 9). Wait, 8 minus 8 is 0. That part is straightforward.

Now, moving to the next digit, which is the nines place. Here, we have 5 minus 1. That should be 4. So, combining those results, the answer is 40 base 9. But wait, let me verify if that's correct. 

Alternatively, maybe I should convert both numbers to base 10, subtract them, and then convert back to base 9. Let me try that method to cross-check.

For 58 base 9: The rightmost digit is 8, which is 8*9^0 = 8. The next digit is 5, which is 5*9^1 = 45. So, total is 45 + 8 = 53 in base 10.

For 18 base 9: The rightmost digit is 8, so 8*9^0 = 8. The next digit is 1, so 1*9^1 = 9. Total is 9 + 8 = 17 in base 10.

Subtracting 17 from 53 gives 36 in base 10. Now, converting 36 back to base 9. Let's see, 9^2 is 81, which is too big. So 9^1 is 9. 36 divided by 9 is 4 with a remainder of 0. So, that's 4*9 + 0, which is 40 base 9. 

Okay, so both methods give me 40 base 9. That seems consistent. But wait, let me double-check the base 9 subtraction again without converting. Maybe I made a mistake in the first method.

Starting from the rightmost digit: 8 - 8 = 0. Then the next digit: 5 - 1 = 4. So, 40 base 9. Yes, that's the same as before. So, both methods confirm the answer is 40 base 9. 

But just to be thorough, let me do the subtraction step by step in base 9 without converting. Let's set it up like a standard subtraction problem:

```
    5 8
  - 1 8
  -------
```

Starting from the ones place: 8 - 8 = 0. No issues there. Then the nines place: 5 - 1 = 4. So, the result is 4 0 in base 9, which is 40 base 9. 

Wait, but in base 9, when subtracting, do we need to borrow from higher digits if the top digit is smaller? For example, if it was 18 - 25 in base 9, we would need to borrow. But in this case, 5 is larger than 1, so no borrowing is needed. So, straightforward subtraction. 

Another example: if we had 12 base 9 minus 3 base 9. The ones place: 2 - 3 can't do, so we borrow 1 from the nines place. Then 12 (base 9) becomes 11 (base 9) with the ones digit being 2 + 9 = 11 in base 10, but wait, in base 9, borrowing 1 from the nines place adds 9 to the current digit. So, 2 + 9 = 11, but in base 9, 11 is 1*9 + 2, so it's written as 12 in base 10, but in the context of the subtraction, it's 11 (base 10) minus 3 (base 10) = 8 (base 10), which is 8 in base 9. Then the nines place was reduced by 1, so 1 - 1 = 0. So, 08 base 9, which is 8 base 9. 

But in our original problem, no borrowing is needed, so it's straightforward. 

Therefore, I think the answer is indeed 40 base 9. Both conversion and direct subtraction methods confirm this. I don't see any mistakes in my reasoning. So, I can confidently say the answer is 40 base 9.
</think>