DC to AC inverter calculations
The values you provide are not sufficient to determine the runtime of the RFID reader, either with or without the laptop. The power brick output specification means that the power brick is able to supply up to 0.4 Amps at 48V, which is a power of around 20W. This implies that the power consumption of the RFID is less than 20W. We have no information, how much below 20W it is. It might be 3W as well as 17W.

The power supply input specification is even less helpful for the question at hand. The power supply is able to cope with input voltages between 100 and 250 Volts, and it promises to not blow a 0.5A (slow-blow) fuse. As 0.5A at 100V is alrwady 50W and 0.5A at 250V is 125W, I am positive that the supply is never going to take that much real power, although at 100V it might consum 50VA apparent power. Typical actual consumptions of a 20W switch-mode supply are up to 2W if the output is not loaded and up to 30W if the output is loaded it the maximum capacity.

A 300W inverter might very well have an idle power consumption of 10W, and a full-load consumption of 420W. If the load to that inverter is 30W, the consumption of that converter could be around 50W from the battery

Your battery provides a total energy amount of 12V * 18Ah = 216Wh. The estimated runtime of the RFID reader alone powered through the 300W inverter and the 20W power brick is thus likely between 20 hours (most energy lost in the converters, total consumption around 10W) and 4 hours (the RFID device utilizes the 20W supply all the time at maximum permissible load, total consumption from the battery around 50W).

The only way to provide better numbers is to actually measure actual power consumption instead of relying on the specs of the power brick.