Question: Assume for this scenario that:

`a = b * c` 

`d = b - c`

I only know the value for `a` and `d` (in this case 0.075 and 239, respectively), and I need to solve for both `b` and `c`. Is this possible to solve given the limited information, and if so what is the best approach to do so?

Answer: 
This is known as a system of *nonlinear simultaneous equations*. In this case, it is very easy to solve the system.

First, write $b$ in terms of $d$ and $c$, where $d$ is known:

$$b = d+c.$$

Substitute this into the first equation:

$$a = bc = (d+c)c = cd+c^2$$

Solve this for $c$ using the quadratic formula:

$$ c^2+dc-a = 0 \implies c = -\frac{d}{2}\pm \frac{\sqrt{d^2+4a}}{2}$$

Substitute the solutions back into the equation $b = d+c$ to find values of $b$.
Yes, there is a solution. I recommend checking the exact form (not approximate) as provided by wolfram alpha.

[Solution](http://www.wolframalpha.com/input/?i=a%20=%20b%20%2a%20c,%20d%20=%20b%20-%20c,%20a%20=%200.075,%20d%20=%20239)

This supports Ed's answer