Deconvolution of integrated data

Hello, I am trying to deconvolve experimental data that can be considered as obtained from the following convolution. G(V)=integral(@E K(E)*F(E-V)), where G(V) is the data as a function of V (specifically, V runs from -10 mV to 10 mV, and G(V) is tunneling conductance that is non-monotonic with two symmetric peaks around V=0), K(E) is what I want to recover (specifically, it is single particle density of states in a superconductor), and F(E-V) is the response function of bell shape centered at E=V (specifically, it is the derivative of the Fermi function). I've tried most functions and found that deconvlucy gives the best result. However, it is not satisfactory as it suffers from the well-known ringing issue. I vaugely imagine that patching the data might improve it but I cant' figure out how. I'd appreciate any advice or reference on this. Thanks.