From Old English hām, from Proto-West Germanic *haim, from Proto-Germanic *haimaz. Cognate with German Heim, Swedish hem, Dutch heem, heim- and West Frisian hiem. Note that this pronunciation is not derived from Old Norse, as is sometimes assumed on the basis of Danish and Norwegian hjem - the pronunciation in Geordie is directly derivable from the Old English form by regular rules. Compare traditional [stjɛn] 'stone' from stān. It can also be found in some other northern dialects like Yorkshire.
hyem (not comparable)
- (Northumbria) home
- [19th c.] 1993, Ned Corvan, “Yer Gannin to be a Keelman,” in Visions of the People, Patrick Joyce 
- Ye’ll be comin’ hyem at neets, with yor fyece all ower black,
- And ye’ll lie an snore aside the fire, and never gis yor crack, [...]
- 1848, Sinks of London Laid Open 
- “He had just come in,” he said, “to see if his mate was come hyem yet; but as he had not, he thought he could guess right weel where he wad be, and wad just step o’er to Brown’s (the gin-shop) and see.”
- 1985, David Wright tr. Geoffrey Chaucer's The Canterbury Tales 
- And so Aah’s cum, and also brought Alan,
- To grind wor corn, and bring it hyem again;
- Aah begs ye de the job fast as ye can.
- [19th c.] 1993, Ned Corvan, “Yer Gannin to be a Keelman,” in Visions of the People, Patrick Joyce