I was going to mention a potentiometer earlier, but did not know your level of knowledge with this stuff.
I'd use something like 1% or better tolerance resistors. If one is 10K make the other one a bit less than 10K.
Let's say the other one was 9.7K for arguments sake. You are 300 ohms away from 10K. So double that and get a 600 ohm 10 turn potentiometer and wire it in series with the 9.7K.
Start of with the potentiometer mid way, i.e. at around 300 ohm, getting the total resistance close to the 10K mark. You then have quite fine adjustment to get the resistances balanced.
Not sure off the top of my head what stock resistance values are available but hopefully the above shows what I mean.