EBV testing here is just positive or negative. They don't do serology to know which virus caused it.I don't think we can, at least in many cases. A lot of common viruses cause a fairly characteristic range of symptoms, but unless a patient is worryingly ill and needs investigations, 'I'm pretty sure it's a virus' often as much as the doctor can say.
There are even two viruses that cause glandular fever symptoms, so unless you're tested – which is unusual, as diagnosis is often straightforward enough that no tests are needed – you couldn't be sure whether it was caused by EBV or CMV.