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This paper proposes a time-domain-based protection scheme for radial and loop microgrid systems with inverter-based resources (IBRs), such as solar photovoltaic (PV) and type-4 wind turbines. The protection scheme is designed to function during both grid-interconnected and grid-isolated modes. The proposed scheme provides an ultra-high-speed sub-cycle directional element aided with low bandwidth communication between relays. Like directional comparison schemes, relays identify whether faults are inzone or out-zone. The directional element is based on time-domain superimposed quantities and Park's transformation algorithms. More specifically, the element calculates the superimposed positive-sequence direct component of transient energy during faults. Superimposed voltage and current quantities are calculated using delta filters and decoupled double synchronous reference frame (DDSRF) filters. The proposed filtering method improves the reliability of the superimposed directional element when IBRs are present. The protection scheme is evaluated on a modified IEEE 34-bus distribution system simulated using an electromagnetic transients program.