A bit of reading later:
TI Single Supply Op Amp Design Techniques says
"Unless otherwise specified, all op amps circuits are single-supply circuits. The
single supply may be wired with the negative or positive lead connected to
ground, but as long as the supply polarity is correct, the wiring does not affect
circuit operation.
Use of a single-supply limits the polarity of the output voltage. When the supply
voltage (VCC) = 10 V, the output voltage is limited to the range 0 ≤ VOUT ≤ 10. This
limitation precludes negative output voltages when the circuit has a positive
supply voltage, but it does not preclude negative input voltages when the circuit
has a positive supply voltage. As long as the voltage on the op-amp input leads
does not become negative, the circuit can handle negative input voltages.
Beware of working with negative (positive) input voltages when the op amp is
powered from a positive (negative) supply because op-amp inputs are highly
susceptible to reverse voltage breakdown. Also, insure that all possible start-up
conditions do not reverse bias the op-amp inputs when the input and supply
voltage are opposite polarity."
So a 7918 negative regulator on the -24V supply should do it and just make sure the polarity is correct...
Cheers, V