Where does the E wire go on a Nest thermostat?

The 'E' typically goes to what is called 'emergency heat' which is often the same as and is connected with the 'AUX' (auxiliary heat) used with a heat pump system. In our area we normally designate this our second stage of heating and it doubles as the primary if and when you need service for an extended period on the outdoor unit. These type of thermostats are connected in a lot of different ways. I would need to see and understand your entire system and how it is designed to work. And I need to know how you want to use energy saving measures. Additionally, I need to know your comfort level demands.