matrices - How to solve a set of equations where the unknowns are a function and some parameters?

I'd like to know how to solve something like this:

$$\begin{eqnarray} f(f(x_2)-f(x_1)) & = & 27.5\\ f(f(x_3)-f(x_1)) & = & 21.6\\ f(f(x_4)-f(x_1)) & = & 15.1\\ f(f(x_5)-f(x_1)) & = & 10.2\\ f(f(x_6)-f(x_1)) & = & 8.8\\ f(f(x_7)-f(x_1)) & = & 8.4\\ f(f(x_8)-f(x_1)) & = & 7.8\\ f(f(x_9)-f(x_1)) & = & 6.4\\ f(f(x_4)-f(x_3)) & = & 46.5\\ f(f(x_5)-f(x_3)) & = & 17.6\\ f(f(x_5)-f(x_4)) & = & 28\\ f(f(x_7)-f(x_4)) & = & 20.1\\ f(f(x_9)-f(x_7)) & = & 22 \end{eqnarray}$$
where I'm looking for $f(x)$ and $x_1,x_2,\ldots,x_9$. It is given that $0