Noise Calculation
There are different ways of looking at the gain. WimRFP gave one way of calculating it. Another way (which I did) was to simulate it. You can also simply go through the equations by putting a voltage source in series with the 10k and working out what voltages you end up with where. What you need to know is how the noise voltage of the 10k resistor is amplified. So, to calculate it you could split the 10k into two 5k resistors, one for each half, so you have 45k/5k. Or you could consider each half to have a gain of 4.5 which adds.
If you simulate it with voltage source in series with the 10k, you will see a gain of 4.5 to the outputs of the two opamps. The phase is opposite, so they add to give a gain of 9.
Bear in mind this is different to the 10x gain you will get when using the actual inputs, which are grounded for your noise analysis. It is the same as a non-inverting versus inverting amplifier where the the equation is 1+Rf/Ri or simply -Rf/Ri depending on which input you use.
In the case of noise, you need to bear in mind whether noise is correlated or uncorrelated. Two separate noise sources such as from two separate resistors are uncorrelated so should be combined by sum of squares. The noise from the 10k is amplified by the two amplifiers and on the outputs of the two amplifiers the noise will be correlated i.e. the noise on one output will have a corresponding correlated inverse on the other. So, when they go through the next stage they add.
I have probably not helped much, I think!
Keith.