The white wires are the thermistor, the small glass bulb on the very end. That needs to be taped against the bottom middle of the bed to read the beds current temperature. You can run it between the others for ease, but it needs to be taped well against the bed. It does not need to be soldered at all.
The bed wires are soldered to the large copper pads. You'll probably need a larger soldering iron like a 100w or so.