It's not a resistor, it's an electrolytic capacitor -
It's not an electrolytic capacitor, well not any more. It WAS an electrolytic capacitor.
The band on the replacement capacitor will be on the -ve side. Get the same or larger voltage rating, and the same or larger capacitance. In smoothing applications like that, generally the larger the better.
Try to get one with the same distance between the pins as the blown one as that will make fitting it much easier, and the diameter should be the same so that it will fit without the relay getting in the way. You may find that the replacement is longer than the original one.
Now that the pins are separate, cut away or pull off the rubber bung, and unsolder the pins one at a time. Use a solder sucker to get enough solder out of the holes that the new capacitor pins will fit. Make sure the new one is the right way round. Push the capacitor down to the board and solder from the other side.
Unfortunately if other components are blown they may be more difficult to see damage on and they may be difficult to diagnose.
If there is a dead short between +ve and -ve, you should try to find what is wrong before wasting time on replacing the capacitor.