Secondary emission from laser produced plasma is governed by the electron distribution function. Therefore, its control is of utmost importance to steer the emission, e.g., of ultrashort bursts of high energy photons and ions for decisive application. Maximum gain is achieved if the laser light absorption by plasma is also maximized. In our theoretical analysis including comparison to recent experiments, we follow this route and study how the energy is transferred from a short laser pulse to the energy of fast ions and X-rays. We make use of ion and K-α emissions, which respond differently to branches of the electron distribution function when we optimize the laser light absorption via structuring of the target surface. Our investigation comprises laser intensities up to 5 × 10²⁰ W/cm² produced with femtosecond near infrared laser pulses and titanium foil targets of a few micrometer thicknesses. In particular, we reveal an energy relaxation process of hot electrons, which determines the observed laser intensity dependence of secondary emission and points to the benefit of target surface structuring in different optimization scenarios.