Education for sustainable development has evolved to include more constructive approaches and a better understanding of what is needed to align education with the cultural, societal, and pedagogical changes required to avoid the risks posed by an unsustainable society. This evolution aims to lead us toward viable, equitable, and sustainable futures. However, computing education, including software engineering, is not fully aligned with the current understanding of what is needed for transformational learning in light of our current challenges. This is partly because computing is primarily seen as a technical field, focused on industry needs. Until recently, sustainability was not a high priority for most businesses, including the digital sector, nor was it a prominent focus for higher education institutions and society. Given these challenges, we aim to propose a research roadmap to integrate sustainability principles and essential skills into the crowded computing curriculum, nurturing future software engineering professionals with a sustainability mindset. We conducted two extensive studies: a systematic review of academic literature on sustainability in computing education and a survey of industry professionals on their interest in sustainability and desired skills for graduates. Using insights from these studies, we identified key topics for teaching sustainability, including core sustainability principles, values and ethics, systems thinking, impact measurement, soft skills, business value, legal standards, and advocacy. Based on these findings, we will develop recommendations for future computing education programs that emphasise sustainability. The paper is accepted at the 2030 Software Engineering workshop, which is co-located with the FSE'24 conference.