Is USB host supported by hardware?

The first place to go, would probably be to the specifications' page on the manufacturer's website or other alternative reputable websites offering the same kind of information.

For a quick check this website doesn't state your device as being supported for USB OTG. The other one GSmarena: Acer Liquid E2, doesn't list this functionality, which most likely means your device doesn't support OTG.

The other ways of checking may be using an application e.g USB OTG Checker ✔ , just as Izzy mentioned, they normally check the presence/absence of certain parameters required for USB OTG to work. For example they check;

the presence of USB Manager, the presence of
android.hardware.usb.host.xml or find the list of connected OTG USB
devices.

It is important to note that this functionality should be supported by the hardware as well as the kernel of the phone.

^{Additionally some users claim the possibility of enabling USB OTG by using tools as StickMount or USB OTG Helper (if the chipset supports OTG and the device doesn't) when rooted , or using a using a usb Y cable (if your chipset doesnt support OTG) to power up pendrive externally}.