As someone else already suggested a charge pump would probably fit the bill here.
Maybe use one element of standard hex cmos inverter as the oscillator and the other five elements
paralleled up through 10 ohm resistors (or whatever) to drive your diode (1n4148  would be fine) /
capacitor networks.
This will give you a rough n* multiplication of the voltage. If you need to regulate that then you
could use a standard 78xx 79xx pair or zeners or just an output capacitor and tweak the
'paralleling' resistors to give you the output you want.

Then again....

I am assuming that the 'long cable run' you are talking about is to an amp at the back of the car
from your head unit ?
and the problem is you get hum / buzz / noise with your current setup so you very sensibly thought
that going balanced would fix it ?
(if not then this won't be much use)

you may be able to solve the problem simply by playing around with the grounding of your system. try
disconnecting the ground wire from the signal cables at one end this might solve your problem
immediately (the noise is actually still there, just a lot less loud)

or even...
don't bother running the circuit at +-18 volts - just use large series caps on the inputs and
outputs of the circuit and run it off 0 and vbat.

Regards,
Simon

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