It's a bit of a pain in the ass process that I've done twice with EE.
The first time, they sent me the eSim pack by post and I scanned the QR code which adds a new data plan to the phone. You've got to be careful not to delete this because each QR-code is valid only once so if you mess up you end up having to get another pack sent to you. After you've done all this, you phone ee and get them to action a 'sim swap' which transfers you account from the physical sim to the data plan eSim on your phone. You can then remove and throw away the old physical sim.
The second time I did it, they insisted I went into the store to do get the eSim pack and have the sim swap actioned there...to be honest, it was easier doing it this way.
The eSIM pack you've got won't be for a different number, but you will have to speak to EE customer services to transfer your account from the physical sim to the eSIM once you've added it to the phone. You can keep your old sim in your phone until customer services have actioned the transfer. Once they do, it instantly disables the old sim (but can take up to a couple of hours to active the eSIM).