Because Microsoft developed Office 2010 strictly for Windows, they released Office for Mac 2011 to serve Apple users. It included Mac-optimized versions of core productivity applications: for text editing. Microsoft Excel for spreadsheets. Microsoft PowerPoint for presentations. Microsoft Outlook for emails and calendars.
Furthermore, searching for "free downloads" of old commercial software online exposes your computer to severe security threats, malware, and legal risks. Microsoft Office 2010 Free Download For Mac Os Sierra
So, even if you found an old Office 2011 installer (the closest relative to Office 2010), it would be a buggy, unsafe experience on Sierra. Microsoft PowerPoint for presentations
If a third-party website claims to offer a direct "Microsoft Office 2010 DMG installer" for Mac, it is highly likely to be designed to compromise your Mac's security. So, even if you found an old Office
Every Mac user has free access to Apple’s native office suite via the Mac App Store.
Works through any browser (Safari, Chrome) on Sierra. Pros: Always up-to-date, file compatibility with other Office users. How to use: Log into Office.com with a Microsoft account. 4. Apple iWork Suite (Pages, Numbers, Keynote)
If you are looking to run this vintage of productivity software on macOS Sierra (10.12), here is a review and guide on what to expect.