I'm trying to solve the following integral equation to find the function $f(x)$ \begin{equation} f(x) = K(x) - \int_0^\infty K(x-t)f(t)dt \end{equation}
where \begin{equation} K(x) = \sum_{i=1}^N c_i e^{-\kappa_i |x|}, \quad \forall i\quad\kappa_i > 0 \end{equation} with the convenient property $K(x-t)=K(t-x)=K(|x-t|)$.
I know that this is an inhomogeneous Fredholm equation of the second kind, however I'm not sure where to begin solving this. Any references and suggestions where to start would be of great help.