My problem is what to do with pin #18, which the datasheet says is Vee, the -10V power supply for the LCD. All of the rest of the pins match up with pinout B from the ks0108 page.
Do I need a separate power supply for the -10v or is this something that I can reference or generate from the arduino?
Pin 18 is a negative voltage source that is used to generate the required negative contrast voltage. Connect one end of a potentiometer to pin 18 and the other end to GND. Connect the wiper to pin 3 and adjust as required. There's a crude diagram of this connection at the lower right of the data sheet in your link.
I think I need a -10Vdc source. What is the best way to add the negative supply voltage?
You are misinterpreting something, doing something wrong, or you have a bad device. Pin 18 is the negative supply source and you adjust it to give -10v by use of the potentiometer. Can you supply a picture of your setup?
Although your datasheet says otherwise you may have a device that requires a slightly positive voltage on pin 3. You could try this: Connect one end of a potentiometer to pin 18 and the other end to +5. Connect the wiper to pin 3 and adjust as required. This is almost the same setup as I gave you in reply #1 except that the potentiometer connection that used to go to GND now goes to +5V. Check out this thread: ***Fixed*** Ks0108 128*64 -> no gfx showing + pictures Atmega 2560 - #5 by floresta - Displays - Arduino Forum especially replies 4 and 5.