Normally you would connect the other half to the unused Rc terminal on the thermostat, if it's used there is an adapter to send power from the air handler transformer without adding a wire.
I see now that this unit lacks an Rc terminal and is not intended by the manufacturer to be used with an external transformer. It might work if you pigtail the transformer to the R terminal, but I'd rather buy different thermostat, as you did. If you buy a thermostat with an Rc, you won't have this problem. And I'd say that applies to most smart thermostats.
I also learned, you should not buy the Nest thermostat E unless you have a c-wire. They say it will work in 85% of homes, but I doubt 85% of homes have a c-wire.