Can I add eSim from T Mobile to my Iphone 14 Verizon Carrier?

As long as your “14” is NOT carrier-locked to Verizon, YES.

See:

Using Dual SIM with an eSIM - Apple Support

How to unlock your iPhone for use with a different carrier - Apple Support

Most likely no 😸 🤯

Not directly without any efforts..

You have options of course:

1. transfer your T mobile number to Verizon network;
2. get Verizon to perform carrier unlock on your iPhone;
3. use 3rd party to do a carrier unlock for the device ;
4. if you are really fed up with Verizon 😤🤠 you may transfer your T mobile number to another carrier who is using Verizon network to provide you services.

These ideas came to my mind but there may be some more .. think creatively. Verizon’s Message+ and also T-mobile’s DIGITS apps may also work for you in some circumstances!

Hope this helps!💐

Language is a wonderful thing.

You and I read exactly the same text and came away w/ two different interpretations:

1) OP desired to add a 2nd line w/ T-Mo to his phone to reside alongside his VZ line.

(this is a relatively trivial task IF the phone is “carrier unlocked”)

2) OP desired to ditch VZ and move to T-MO.

Either (or neither) might capture the OP’s true intent. 🤷🏼