New facilities of the 2020s, such as the High Luminosity Large Hadron Collider (HL-LHC), will be relevant through at least the 2030s. This means that their software efforts and those that are used to analyze their data need to consider sustainability to enable their adaptability to new challenges, longevity, and efficiency, over at least this period. This will help ensure that this software will be easier to develop and maintain, that it remains available in the future on new platforms, that it meets new needs, and that it is as reusable as possible. This report discusses a virtual half-day workshop on "Software Sustainability and High Energy Physics" that aimed 1) to bring together experts from HEP as well as those from outside to share their experiences and practices, and 2) to articulate a vision that helps the Institute for Research and Innovation in Software for High Energy Physics (IRIS-HEP) to create a work plan to implement elements of software sustainability. Software sustainability practices could lead to new collaborations, including elements of HEP software being directly used outside the field, and, as has happened more frequently in recent years, to HEP developers contributing to software developed outside the field rather than reinventing it. A focus on and skills related to sustainable software will give HEP software developers an important skill that is essential to careers in the realm of software, inside or outside HEP. The report closes with recommendations to improve software sustainability in HEP, aimed at the HEP community via IRIS-HEP and the HEP Software Foundation (HSF).