The new generation of deep photometric surveys requires unprecedentedly precise shape and photometry measurements of billions of galaxies to achieve their main science goals. At such depths, one major limiting factor is the blending of galaxies due to line-of-sight projection, with an expected fraction of blended galaxies of up to 50 per cent. This proof-of-concept work explores for the first time the use of deep neural networks to estimate the photometry of blended pairs of galaxies in space-based monochrome images similar to the ones that will be delivered by the Euclidspace telescope under simplified idealized conditions. Using a clean sample of isolated galaxies from the CANDELS survey, we artificially blend them and train two different network models to recover the photometry of the two galaxies. We show that our approach can recover the original photometry of the galaxies before being blended with ̃ 7 per cent mean absolute percentage error on flux estimations without any human intervention and without any assumption on the galaxy shape. This represents an improvement of at least a factor of 4 compared to the classical SEXTRACTOR approach. We also show that, forcing the network to simultaneously estimate fractional segmentation maps results in a slightly improved photometry. All data products and codes have been made public to ease the comparison with other approaches on a common data set. See https://github.com/aboucaud/coindeblend.