Hi Bob, a couple of options,............
1/ If you are not concerned about trashing the original tires (for posterity/originality) , you could strip the tires, and replace with some Paul Gage urethanes.....he makes these (in black) to fit the "Cuc" wheels, which are identical to those on your 2E.
These will grip well on your Carrera track, and will last ages. These will work best if glued and trued on your existing wheels.......they are easy to find/order on his website.
2/ You could buy some silicone coated sponge "Pro Track" tires (mounted on wheels) for 1/8th axles. (Professor Motor and others carry these in both .820 and .815 diameters). You will however need to buy a 1/8th drill blank axle for this option, and replace the "taper lok".
These will also grip well on Carrera track, and as they are already trued, they will be "bolt on" (other than replacing the axle).
The silicone coated sponge are softer and have more compression than the urethanes, and will offer more compliant handling than harder urethanes.
Cheers
Chris Walker