Let's do some dividing.  330 by the number of cents in
the various coins:

330/100 = 3.3
330/50 = 6.6
330/25 = 13.2
330/10 = 33
330/5 = 66
330/1 = 330

To have 18 coins, since 13.2 is closest to 18, one of the coin types
has to be quarters.

Hey! 13 quarters is $3.25 and 5 more cents is 18 coins and that's $3.30.

So there's a solution you didn't have.

Try 1 less quarter, that's 12 quarters or $3. Can we make the 
remaining 30 cents with 6 of the same kind of coin?  Yes 6 nickels!

That's the solution you have.

Try 1 less quarter, that's 11 quarters or $2.75. Can we make the
remaining 55 cents with 7 of the same kind of coin?  Nope!

Try 1 less quarter. That's 10 quarters or $2.50.  Can we make the
remaining 80 cents with 8 of the same kind of coin?  Yes, 8 dimes!

That's another solution you didn't have.

No use to try for 9 quarters.  That's $2.25/ leaving $1.05, No way
to have 9 of the same kind of coin totaling that.  



So there are three solutions

10 quarters and 8 dimes.
12 quarters and 6 nickels.
13 quarters and 5 pennies.

Edwin