Connect the GND pin to +10V and power pin to 16V for the PIC
Ha-ha, it is the right answer on such unspecified question!
Is it really that difficult to "subtract" (is that the right usage?) 10v DC?
It is ungrateful work to search for universal abstract "technical" solution for unspecified problem.
On your assumption that with hypothetical "substractor" the things will be "better" I can say that 0.016V resolution is already not bad.
Try to respect our efforts little more by specifying more conditions/requirements.
At first - 1) what is the original (real?) problem that needs to measure battery voltage?
2) Justify requirements for precision in terms of absolute accuracy and resolution.
3) Specify additional conditions: temperature range for operation, calibration is intended or device must work right after assembling, expected price (I mean $$$), e.t.c.
Start to think from selection of appropriate voltage reference. Check parameters of integrated band gap and the _real_ ability of ADC in selected PIC for example. Try to find voltage reference with desired characteristics. Check it's price. Roughly: you will add errors of each used voltage reference to resulting measurement error. The same is true for precision of resistors, but resistors are much more stable devices comparing to semiconductors.
The simplest "substractor" you have to know about is a zenner-resistor divider. You can replace Zenner diode by shunt-type voltage reference (am not sure there is such for 10V value). Think about resistor in this circuit not only as a lower half of divider but also as a current limiter/setter for upper voltage source - changing input voltage will change current through voltage reference device... (Hommage a Sacher-Masoch: try to replace resistor by current source, check its lowest operational voltage)
Next fantasy: add a temperature sensor and build 2D calibration table for used Zenner. (Some voltage reference devices have an integrated heater for temperature stabilization)
Fantasy #3: replace Zenner diode by negative LDO voltage regulator. I do not know if "negative" series voltage reference chips are exist.
More universal approach of course is to use operational amplifier (consider voltage offset) to substract/sum signals. See attached schema:
While it will work as you wish I consider it as ineffective usage of additional ICs to achieve better precision (see my previous post).
Another way - search for specialized/suggested solution from different vendors for your exact task (in most cases it will be an appropriate ADC). There are plenty of battery monitoring IC in the world.
