Help with a Nest E install on a old HVAC system
Somebody misplaced the blue wire from the system to the thermostat

It appears that the previous installer, for some bizarre reason, connected the blue wire and the red wire in the cable from the indoor unit to the thermostat to the fat red R wire coming from the indoor unit.  Luckily, between the wiring diagram on your unit showing the fat brown wire as the indoor unit's C wire, and the fact we can trace the air conditioner control from the Y wire from the thermostat, to the red wire in a cable, with only a white wire returning to join up with that brown C wire, means that we can simply swing the blue wire from the thermostat over to join with the other wires connected to the fat brown C wire and put a replacement wirenut on the junction of the red R wires in order to get everything in order for your Nest to work.