This is the equation:
\begin{eqnarray*} f\left(e\right) & = & -r\left(e\right)\left(1+\int_{E}\cos\left(s\left(e\right)-s\left(e'\right)\right)de'-\int_{I}\cos\left(s\left(e\right)-s\left(i\right)\right)di\right) \end{eqnarray*}
All functions are one-to-one and range between $-1$ and $1$. The functions $r$ and $s$ evaluate to constants not to other functions. However, they are not linear but more like a hash. The subscripts on the integrals denote the domains.
Edit
I began by expanding the integrals to isolate terms. For example, what follows is an expansion of the middle term of the right-hand side.
\begin{eqnarray*} \int_{E}\cos\left(s\left(e\right)-s\left(e'\right)\right)de'=\cos\left(s\left(e\right)\right)\int_{E}\cos\left(s\left(e'\right)\right)de'-\sin\left(e\right)\int_{E}\sin\left(s\left(e'\right)\right)de' \end{eqnarray*}
How can I evaluate these integrals?