The interaction of anionic silica nanoparticles (Ludox LS30) with non-ionic surfactant decaethylene glycol monododecylether (C12E10) without and in the presence of an electrolyte has been studied by small-angle neutron scattering (SANS) and dynamic light scattering (DLS). The measurements have been carried out for fixed concentrations of nanoparticles (1 wt%), surfactant (1 wt%) and electrolyte (0.1 M NaCl). In SANS, each of these nanoparticle-surfactant systems has been examined for three different contrast conditions where both (nanoparticle and surfactant) as well as individual components (nanoparticle or surfactant) are made visible. It is observed that the nanoparticle-surfactant systems behave very differently without and with the electrolyte. In the absence of salt, the C12E10 micelles form micelle decorated core-shell structures by adsorbing on the nanoparticles. On the other hand, the adsorption of surfactant micelles on nanoparticle is completely suppressed in the presence of salt, leading to the depletion-induced aggregation of nanoparticles. These results have also been corroborated by the DLS data. We thus show that the ionic strength of solution can be used to tune the interaction of ionic silica nanoparticles with non-ionic surfactant.