magnetic synchro angle revolver
First option, digitize ASAP and numerical process, is by far the best.

Analog filters are cumbersome and difficult to tune and keep tuned against components drifts and tollerances.  

You have two unknowns, T and E and two signals to work on A and B, you should be able to work them out but do your marh first.

Definitely go digital, will be both cheaper and better performance.



Edit following Abolfazl N comment:
Your concerns are legitimate but I'd go digital all the same, with a little simple analog help though.

Those two carriers are just over 23dB apart in amplitude but only one octave frequency separated. Trying to improve this the analog way involves a fourth order low Q  filter (4 x 6dB/oct x 1oct = 24dB) just to bring them to the same amplitude.

Otherwise a high Q second order bandpass could also do.

Low Q high order requires quite some hardware and probably individual tuning of each build unit.
High Q bandpass is simpler but may be prone to bring in some ringing on transients, needs tuning all the way and should be carefully studied considering input signal dynamics (i.e. dT/dt e dE/dt).
Finally both could suffer from possible carrier frequency drift.

On the other hand improving range to accomplish the saturation free first harmonic only takes a 24dB / 6dB/bit= 4 bits wider ADC i.e. you could switch from a 12 bit to a 16 bit, signals are relatively slow and sampling rates needed are quite within reach at those width.

Once on the digital domain you can adaptively filter, phase lock to carrier, I/Q demodulate or whatelse you plan to do to recover your informations.
It all can be easily reconfigured, changed, adaptively tuned with the greatest easy just changing code, I would never give away this freedom for anything in this world.
You have no limits, but just fantasy to keep improving your measure.



Finally I could say that, as usual, virtue lies in the middle: I'd rather wire in a simple, troubleless first order first order highpass or at most a moderate Q bandpass.
Doing so I could gain some 6dB a.k.a. 1 bit resolution and then happily go digital.



P.S. not mentioned above but do not forget anti-alias filter, but again I'd rather oversmaple as much as possible, keep HW simple and tune free and then decimate samples.