A 25 watt iron is PLENTY big for joining 18 ga wire. If you've got a new iron, you need to tin the tip before you can effectively solder with it. Let the iron get really hot, wipe the tip off with a moist cellulose sponge then coat the tip with solder and wipe the excess off with the sponge. It should have a thin layer of solder all over it and is now ready for use. The tips on the cheaper irons are sometimes hard to tin for some reason. It sometimes helps to rough them up with some emery cloth first but I've run across cheap chinese tips that will not tin completely no matter how much flux and solder you throw at them. And 60/40 rosin core is perfect for your purpose.

One thing I've found that speeds up the soldering process is to let the iron get good and hot then just touch it briefly with the solder to put a small drop of molten solder on the tip. Then place the wires in this drop, using it to transfer the heat. If you just place a dry tip on the wire there's not much surface area contacting the wire thus not much heat transfer. The goal is to transfer as much heat as quickly as possible. Quick heat transfer aids in localized heating so you don't end up holding the iron on the wire for 30 seconds heating six inches of wire and messing up your insulation (and causing your shrink wrap to shrink too soon!) . Using this method (very hot iron and drop of solder to transfer heat) it should only take a couple seconds to heat the joint enough to touch the solder to the wire and it will instantly flow. Hope this helps.