I'm arriving on a different airline than I'm leaving, do I need to pass through security again or can I transfer flights airside at this airport?
When you arrive at Eindhoven airport you disembark the airplane, get a short walk under a roofed walkway and go immediately to the baggage claim area and from there you reach the main hall, along the red path in the picture.
If there is any passport control because you are coming from outside EU, it is done on the same path. There is no direct physical connection for passengers between this route and the gates. You need to go again through security checks from the entrance.
If you have checked in baggage, you will also need to pick it up and check it back in.
Since you have a self transfer, you most likely won't have a choice, but to go to the landside on arrival. Eindhoven Airport is fairly small and I don't think they have options for a connection (I'm not 100% sure).
A while back I had a layover there, all passengers on board needed to leave the plane for refuel. They pack everybody who didn't have Eindhoven as the final destination in a warehouse looking room for about 40 minutes before we boarded again. However, I understand that this was possible only because everybody was traveling on the same plane with the same airline.