|if I understand your equations correctly, at 18 volts, a 1/8 watt resistor can handle 7 milliamps?
ok, but - you are leaving out the resistance
10 ohm @ 18V?
18/10=1.8*18=1800mA*18V=32,400 mW = Smoked.
10k @ 18V?
18/10,000=1.8mA*18=32.4 mW = Fine.
And you gotta consider, that's the power of the resistor's rated capability
... In your amp no resistor would see 18V unless you're using it to drop power (dissipate for no reason than you need a lower voltage) it'll never see all 18V unless something went terribly wrong in your amp.
Your current-limit resistor on your LED probably sees the most work. Hey, let's find out!
A resistor divider across the rails to make your virtual ground. So if you went 2x4.7k that'll be 9.4k... while this is about the same as the 10k LED resistor, in a voltage divider (series) each resistor drops the V, in this case half of it, so really each resistor is only dissipating 18/9400=1.91mA*18=34.4mW/2=17.2mW.
So yea, the LED resistor is dissipating more. Sneaky, ain't it?