My office network uses enterprise security authentication and I want to login to this network and share it via WiFi and Ethernet of the GL-MT1300. Is it is possible to login to this enterprise security WiFi network using the GL-MT1300?
No the Mt1300 (or the MT300N-V2 for that matter) will not connect to EAP. You would be better served by an AR750S
So, AR750S will do EAP right? Is the difference between AR750S and GL-MT1300 only wifi speed? Does AR750S separate radio for WAN and LAN side? For example, If WAN side is connected using 5GHz WiFi, is it possible to connected LAN side at 5GHz WiFI as well?
does GL-AXT1800 support EAP?
Do you mean connecting to EAP network? Yes it does
Still haven’t bought one??? 
Of the newer models now GL-AXT1800 - Slate AX and GL-AX1300 will both support EAP.