I am trying to install a ritetemp 8050C model thermostat to replace the Janitrol thermostat that came with my Goodman-Janitrol two-stage, heat pump system. There is an "E" terminal on the Janitrol unit (seven wires) but no corresponding terminal on the ritetemp unit(six wires). What is the function of the "E" wire on the Janitrol unit? Do I need to connect this wire to anything on the ritetemp unit?

I think you will be better served if you leave it alone. Put the original thermostat back on and call it a day. Next option is to call a qualified contractor and have them fix it correctly. You can damage your heat pump by improper wiring. Do not take the risk it is not worth it.