What the output type means for wiring
The Omron E2E2-X2B1-M1 is a PNP (sourcing) proximity sensor — when it detects a target, it switches the output positive relative to the common. That means it drives a PLC sinking input directly without a pull-up resistor, which is the standard for most 24 VDC control systems. If your panel uses NPN (sinking) inputs, this sensor won't match without a converter.