This paper presents experimental measurement of neutron flux from an AmBe source using a stilbene organic scintillator and subsequent mathematical processing of the measured data. The neutron energy spectrum was reconstructed by solving a Fredholm integral equation of the first kind using maximum likelihood expectation maximization (MLEM) and a novel B-spline-based MLEM-BS method with regularization. Bootstrap resampling was applied to estimate confidence intervals. Results demonstrate successful neutron spectrum unfolding, reduced noise sensitivity of the spline approach, and good agreement of the reconstructed spectrum with the ISO reference standard.