How can I find the Van der Waals constants (a and b) without any critical values? I'm given a container of gas that is kept at constant temperature, and whose volume is decreased by applying pressure, from A to E, as the graph shows. I am given the temperature, the total moles in the container, and the following data:
At B the molar volume is 1.153, and the pressure is 17.76.
At C the molar volume is .8167, and the pressure is 17.76.
At D the molar volume is .032, and the pressure is 17.76.

Given this data, and I emphasize, only this data (no critical P, T, or Vmolar), find the van der Waals constants, a and b, for the gas. 

I've been working on it for 3 hours and so far all I can come up with is a single equation in terms of a and b at point B: 17.76=RT/(Vmolar-b) - a/Vmolar^2
At point C, the equation would be the same as what I came up with for B, since the temperature and pressure remains the same as B, and we're in the region of co-existence, so Vmolar is at its maximum for the gaseous phase and therefore also is the same as in B (any further increase in Vmolar causes precipitation). 

Any and all help is greatly appreciated.
I would approach this a little differently.  I would integrate the pressure between $V_D$ and $V_B$, such that the average pressure is 17.76 bars:  $$\frac{\int_{V_D}^{V_B}{PdV}}{(V_B-V_D)}=17.76$$or,
$$17.76(V_B-V_D)=RT\ln{\frac{(V_B-b)}{(V_D-b)}}-a\left[\frac{(V_B-V_D)}{(V_B-b)(V_D-b)}\right]$$
This would provide an equation for expressing a in terms of b.  So the pressure could then be expressed exclusively in terms of b.  Then, to determine the value of the constant b, I would set $P(V_B)$ equal to $P(V_D)$ and solve the resulting equation for b.