The Nuclear Measurement Laboratory (LMN) at CEA Cadarache in France uses a high-energy electron linear accelerator, LINAC (9-21 MeV), to characterize nuclear waste drums. It enables to explore new examination modalities, such as active photon interrogation or dualenergy CT to scan large concrete objects with diameters up to 140 cm. These techniques require precise awareness of the photon spectrum emitted by the LINAC. However, direct measure of this photon energy spectrum cannot be achieved because of the accelerator pulses causing detector saturation. During the last few years, a large number of indirect methods has been developed. From an experimental point of view, the simplest indirect method for spectrum estimation method is ransmission measurements. Because it can be set up easily and accurately using an ionization chamber as well as an appropriate screen. The obtained transmission curve depends on the photon energy spectrum, which can be estimated using inverse models. In this paper, we present the development of a numerical model to determine the energy spectrum from an attenuation curve via transmission measurements which combines two types of inverse models: a continue model and a discrete model. We validate this tool using a test spectrum and its transmission curve obtained via Monte-Carlo simulation. This qualification allowed us to determine its sensitivity (signal-to-noise ratio, SNR) in order to have a good convergence. We show that if the SNR is less than 4%, we have a good estimation of the photon energy spectrum. Then, it was experimentally tested with a transmission curve obtained at the laboratory.