The solar wind blows an immense magnetic bubble, the heliosphere, in the local interstellar medium (mostly neutral gas) flowing by the Sun. Recent measurements by Voyager 2 across the termination shock, where the solar wind is slowed to subsonic speeds before entering the heliosheath, found that the shocked solar wind plasma contains only approximately 20 per cent of the energy released by the termination shock, whereas energetic particles above approximately 28 keV contain only approximately 10 per cent; approximately 70 per cent of the energy is unaccounted for, leading to speculation that the unmeasured pickup ions or energetic particles below 28 keV contain the missing energy. Here we report the detection and mapping of heliosheath energetic ( approximately 4-20 keV) neutral atoms produced by charge exchange of suprathermal ions with interstellar neutral atoms. The energetic neutral atoms come from a source approximately 60 degrees wide in longitude straddling the direction of the local interstellar medium. Their energy spectra resemble those of solar wind pickup ions, but with a knee at approximately 11 keV instead of approximately 4 keV, indicating that their parent ions are pickup ions energized by the termination shock. These termination-shock-energized pickup ions contain the missing approximately 70 per cent of the energy dissipated in the termination shock, and they dominate the pressure in the heliosheath.