Your best bet is to solder the wires back where they came from and restore your headphones to normal function.
The two wires were most likely connected together on the PCB - and connected to other things on the PCB.
"The golden wire" is a stranded wire insulated with lacquer.
Do the following to get things reconnected:
Twist the strands of the "golden wire" back together.
Get a large blob of melted solder on the tip of your soldering iron.
Poke the end of the stranded wire into the blob of solder.
Hold the end of the stranded wire in the melted solder blob for a while - many seconds will be needed until it starts to smoke.
Pull the wire out of the solder. The lacquer should have burned off. If not, repeat steps 2-4.
Tin the wires (stranded and black) and solder them back where they came from.
Your headphones should work again.
As mentioned in the comments, if you want to play with a microcontroller then you should find one intended for tinkerers. The various Arduinos are good for beginners
I would go a step further and suggest you get a book on basic electricity and electronics. At the very least look up some good (written, with diagrams) tutorials on electricity and electronics.
Starting out with microcontrollers is great, but you won't be able to do much with one if you can't even connect an LED.