I have an existing standard light switch that controls a single two-plug outlet. I would like to replace the switch with a dimmer switch.

The dimmer instructions expect two black wires and two white wires (and a ground) in the box, but there is only a single white and a single black (and a ground). The white wire and black wire come from the same larger white wire, where the first layer of sleeve has been removed to show the two of them.

How do I wire this up correctly?

Instructions

Wall Box

Dimmer Switch