Identify empty xml files?

I have a requirement to identify and write all xml file names which are empty to a text file for reporting purpose. Empty , here means the xml file has the usual header tag <?xml version="1.0" encoding="UTF-8"?> followed by an empty open and close tag.

Sample file: 1)

<?xml version="1.0" encoding="UTF-8"?>
<STBTests>
</STBTests>

2)

<?xml version="1.0" encoding="UTF-8"?>
<UMTTests>
</UMTTests>

There are no data in the xml files apart from this. Any suggestions on how to approach this would be great.