Documents open in Office 2010 on PC with both Office 2010 and Office 2019

Co-installations of Office 2010 and 2019 are supported according to the Microsoft support article Install and use different versions of Office on the same PC, but you must meet several requirements, the relevant one being:

Install earlier versions of Office first. For example, install Office 2010 before installing Office 2019...

Based on your question you installed Office 2010 second, which is why you're having problems. Correct this by running a repair installation of Office 2019. If that fails, uninstall Office 2019, make sure Office 2010 is working properly, then reinstall Office 2019.

Additional Information

• Office 2010 and Office 2013, 2016, or 2019 side by side