Both Office 2010 (including Outlook) and Live Mail should work on Windows 10, but Live mail has been end of life for almost 4 years now and Office 2010 will go end of support in October 2020.
You may want to switch to a supported product (Office 365 or Office 2019 if you want to go paid) or you can choose from several free email clients such as the built-in email client for Windows 10, MailBird, or ThunderBird.