In views, how do I show posts from this calendar day, ten years ago?
Like you did, create two filters for the date range and then use the following values

-10 years midnight 
-10 years +1 day midnight


Remember to select 

An offset from the current time such as "+1 day" or "-2 hours -30 minutes" 


If you want to do this programmatically you can create a date filter and set the actual date values from code for the filter range.

You can create the date filter and set the filter value programmatically like the following

How do I programmatically render a view that has exposed filters?