This work utilizes a combination of theory and experiments to explore the adsorption of two different cationic polyelectrolytes onto oppositely charged silica surfaces at pH 9. Both polymers, poly(diallyldimethylammonium chloride), PDADMAC, and poly(4-vinyl N-methylpyridinium iodide), PVNP, are highly charged and highly soluble in water. Another important aspect is that a silica surface carries a relatively high surface charge density at this pH level. This means that we have specifically chosen to investigate adsorption under conditions where electrostatics can be expected to dominate the interactions. Of specific focus in this work is the response of the adsorption to the addition of simple salt (i.e., a process where electrostatics is gradually screened out). Theoretical predictions from a recently developed correlation-corrected classical density functional theory for polyelectrolytes are evaluated by direct quantitative comparisons with corresponding experimental data, as obtained by ellipsometry measurements. We find that, at low concentrations of simple salt, the adsorption increases with ionic strength, reaching a maximum at intermediate levels (about 200 mM). The adsorption then drops but retains a finite level even at very high salt concentrations, indicating the presence of nonelectrostatic contributions to the adsorption. In the theoretical treatment, the strength of this relatively modest but otherwise largely unknown nonelectrostatic surface affinity was estimated by matching predicted and experimental slopes of adsorption curves at high ionic strength. Given these estimates for the nonelectrostatic part, experimental adsorption data are essentially captured with quantitative accuracy by the classical density functional theory.