How do retroviruses exit the cell
Retroviruses, like many other enveloped viruses, exit the cell by a process called budding. The virus uses the host machinery for producing transmembrane proteins to enrich areas of the host cell membrane in viral transmembrane proteins, and co-opts a host process for releasing vesicles.  You can see budding illustrated in the context of the life cycle of HIV in this figure from Murray Medical Microbiology.



The process has been studied in some detail in HIV and other retroviruses.