Whether your phone has electronic or physical SIM is irrelevant, but roaming means using your phone on foreign networks. That can be for voice calls, texts messages and/or mobile data. Receiving texts is free globally, but if you don't want your phone to roam via the EE SIM at all, then disable that SIM in your phone's settings for the duration of your trip.
You could divert all incoming calls to voicemail and set an extended absence message to advise why. Disable mobile data & data-roaming on whichever SIM you don't want to use - or set the other one as primary. Set whichever SIM you'd prefer, as primary for outgoing texts - or don't send any.
I'm not sure whether flight mode can be set for each SIM independently - your phone's settings may differ.
