Here's a clever way to do it. But your teacher probably won't like it:

$1.25 in all nickels would take 125/5 = 25 nickels. But since there are only
18 coins, 25-18=7 of them must be dimes.  The other 18-7=11 must be nickels.

But your teacher probably wanted you to do it this way:

Let n = the number of nickels
Then 18-n = the number of dimes

The value of the n nickels is $0.05n
The value of the 18-n dimes is $0.10(18-n)

If you add those two you must get the total amount of money.

$0.05n + $0.10(18-n) = $1.25

Take away the $'s and multiply through by 100

5n + 10(18-n) = 125

Solve that for n.  Then subtract from 18 to get the number of dimes.

Edwin