Identify resistor with faded color bands
If the resistor is still OK, though faded, you could measure its value.  If it has failed, then you pretty much have to find a schematic with values, or another (identical board) where the resistor is still readable.

Assuming the resistor is OK:

Given how over heated that resistor looks, I'd be afraid of it falling apart if I tried to unsolder it completely.

What I'd do it use a pair of side cutters to clip the lead on one end, then raise it just a little so that the connection is open. Then I'd use a multimeter to measure the resistance.

Clip the lead right at the through hole.  Be careful when you clip it not to wiggle the part around too much.

If you don't have a small pair of side cutters, you might use a pair of toe nail clippers (the clippers, not the nail scissors.)

In any case, clip the lead flush to the board.

Once you have the value, push the resistor back down so the leg makes contact with the clipped spot, then solder the leg back together.  That lets your circuit keep working until you get a replacement.

Keep in mind the power rating.  Under no circumstances should you use a resistor with a lower power rating.  Use a higher power rating if you have room for it and can make it fit.  The one you have seems to be a little on the small side (power rating wise,) so a higher rating would be a good thing.