A good Indicator for determining covid-19 and influenza A/B

The initial symptoms of covid-19 and influenza are very similar.
Is RT-PCR or antibody testing the only way to distinguish between these two infections?

Sapienza Univ. of Rome’s group has reported that the absolute count of monocytes, a type of leukocyte, is a good discriminating index between the two.
https://www.infezmed.it/media/journal/Vol_28_4_2020_9.pdf

If the absolute count of monocytes is 0.35×10^3/mL or more, COVID-19 can be distinguished from influenza A/B. AUC=0.68 (sensitivity=0.992, specificity=0.368)

This strongly suggests that covid-19 and influenza A/B have different immune responses.