Is there a way I can connect 2 wires without solder?

Electrical tape?

*Although I’m not positive… This is more a guess for you to research as an option so please don’t just go do it.

Sure. Twist the wire ends together and use a wire nut. You can get wire nuts in various sizes at any hardware store.

I’d twist them together firmly and then put shrink wrap around it.

But what @CWOTUS said seems smarter.

Can I use you as a reference sometime, @Mariah? That’s the most ringing endorsement I’ve had in years.

And I would still use a wire nut. Taping it afterward is a “belt and suspenders” thing that some people do, but if the pieces are properly sized that shouldn’t be a consideration.

Twist on wire nuts if you have the space.

Personally, I am a big fan of wire nuts too. If space is a concern and you wind up just twisting them together, make sure you twist them tightly; pliers may be needed.

I have a whole jug of wire nuts. Can I send you some? My favorites are the yellow ones. They’re very pretty.

Superglue?

Use wire crimps:
http://i00.i.aliimg.com/photo/v0/427638864/Wire_Crimping_Terminals.jpg

http://www.bmotorsports.com/download/products/wiring/Crimp-Poster-Guide.png

Once again… I didn’t read the whole question. Sorry for the dumb answer. CW answered it correctly so we don’t have to

Wire nuts: Certainly a standard way to interconnect wires over a certain range of gauges, not too big or small. You should at least have an inexpensive wire stripper and know how to use it without damaging the copper conductors. Better to strip stranded wire longer than solid wire of the same gauge & finger-twist before applying wire nut. Make sure the wire nut is small enough to actually twist conductors together and not just insulation instead.

Superglue: Seems like a bad idea except as a very-short-term McGiver-type scenario, and even then it’s got a high risk of failure as it probably becomes a dielectric (non-conductor) when it dries. It would need to be scraped off solid wire before using it again. Stranded wire, I would guess, will be gummed up with hardened glue at copper contact points in the braiding and probably raise the wire’s resistance. (I wonder if it burns off with a soldering iron…?)

@itsjustcruel: Can you give us more details about,The solder has come off the joint between two wires… How big are the wires? Can you tell how the wires were mechanically attached to each other before they were soldered (usually the case)? Do they attach to another metal part (soldering lug) in common?

If it’s a battery wire that’s come off a battery you might need more like a welder than a soldering iron to re-attach it !

What is the gauge of the wire?

Crimps are used exclusively to install car stereo systems and aerospace wiring.