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: 
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
Rewrite your two equations:
$$
\begin{cases}
.075 = b\times c \\ 239 = b-c
\end{cases}
$$
Now solve the second equation for $b$ so that $b=239+c$. Plug this into the first equation in place of $b$:
$$
.075 = (239+c)\times c
$$
Do you know how to solve quadratic equations? Once you have the possible values of $c$, plug those back into our equation for $b$ to get the final answer. This method is called eliminating a variable by substitution.