This is great topic, I am posting some excellent links covering your research interests, the first link covers a thorough literature review paper on "Employer branding and its influence on employee retention", the second one is titled " How Does Employer Branding Increase Employee Retention?", the third one is titled " Employer Branding: A Tool For Employee Retention, please take time to read the three papers and try to extract the key findings, all the best in your field of research.
I would hazard to say that employee retention is more likely to ensue directly from employee engagement than from employer branding. After all, a company’s "reputation" does not necessarily represent reality. That said, much depends on what employer branding entails.