does anybody know if the catalyst switch 4510R-E works with only one Supervisor Engine plugged?
Yes it does. Both the 4507 and 4510 allow for redundant supervisors but there is no need to have the redundant supervisor for the switch to run.
Yes it will work with only one Sup but Cisco Catalyst 4510R-E supports redundant supervisors to minimize downtime.
this link will help http://www.cisco.com/en/US/products/ps9297/index.html
Supervisor engine is required for the 4510-r switch to work as the ios is present in the supervisior engine ony.