Thanks for trying to tidy this up, but the Wolds Way starts in Yorkshire, not Lincolnshire: https://www.openstreetmap.org/relation/13222021#map=13/53.7060/-0.4605 .  See https://www.nationaltrail.co.uk/en_GB/trails/yorkshire-wolds-way/route/ .  E2 doesn't exist on the ground in the UK so is unverifiable, but there is presumably a bit of it that isn't part of any National Trail between Barton and Hessle.  Similarly there's apparently a short bit of the Wolds Way that isn't part of E2 at the south end, and possibly also at the north end (though I'm not exactly sure where the Wolds Way ends there's a large acorn, so it should be verifiable.
Note that https://www.openstreetmap.org/relation/13222021 is neither the "Worlds Way" (as you have spelt it) nor the "Wolds Way".  https://www.openstreetmap.org/relation/78028 is the Wolds Way.