SQL Server 2008 R2 Edition Upgrade Process
You will need to use SQL Server 2008 R2 Enterprise Edition media to perform the in-place edition upgrade.  I am unaware of any option available that allows you to perform an edition upgrade without a version upgrade when using media from a different SQL Server version.

Will your licensing agreement cover this?  That wholly depends on your licensing (though I highly suspect it won't), but that question is best sent to your license partner/reseller.

If you have a MSDN license, you may still be able to pull down the binaries for SQL Server 2008 R2, so that would be one way to get the required media.