The wire which has come unsoldered is a "coaxial wire" this means that it is two wires in one package… the center conductor is your positive or hot wire. The braided, or outside surrounding wire is your negative, or ground wire. Ok, for the novice to know which wire goes where… plug your guitar cable into the jack, and look at the prong on the jack which is touching the end, or "tip" of your cable. Trace this prong back to its solder lug, (the place where it was soldered. This is where your center, or hot wire goes… You can trace the other lug, to make sure it goes back to the part of the jack which is touching the base, or sleeve, of your cable end. Solder both wires into place, using a 10 or 15 watt soldering pencil, and some very fine resin core solder… you can get this stuff at radio shack. Heat up the lugs on the jack, untill the solder is nice and flowing. Sling the wet solder out of the holes in the lugs… now strip back a little insulation from the hot wire, and tie it in a little knot through the hole in the lug. do the same to the ground wire. Make sure that your soldering pencil is nice and hot… oh, before you plug the pencil in, you need to dress the tip of the pencil… get a file, or some medium sandpaper, and knock all of the chrome off of the new tip… then plug it in, get it hot, and melt enough solder onto the tip to get it nice and covered… this is called "tinning" Place the tip of the soldering pencil exactly in the vortex where the wire, and the solder lug meet, and feed solder into the opposite side. (dont feed the solder into the tip of the pencil, this is the most common mistake in soldering. The capilary action of the heat from the soldering pencil, will draw the solder all through the wire, and lug, making a nice wet connection. feed as much solder into the lug as it takes to make a nice flowing joint. Let it cool a few seconds before you touch it. lol. There ya go! no charge! Matt