Install an unfinished wooden floor transition, stain to match.
Homey Depot sells them.

That’s a tough one. It looks like if you removed the narrow course to the left of the gap, youd have a gap about 1.25-1.5 the wide of one course.

Id either take that thin course out to the left of the gap, install a a new course and then put a transition in like has been said OR I’d try to remove a few courses and try to narrow the width of those courses to close the gap.

Either way it’s not going to be perfect, and it might annoy if…if that’s the case, remove the tile from the smaller of the two rooms and redo…

Goodluck, mudshark

Put a carpet landing strip on it. Everyone loves a landing strip.

The only way you’re making that look right, is with another row of wood and a reducer on top of the tile.

This.^^^

Which ever side is lower, have your tile guy run a half tile length to help close up the gap a little, you're not going to find/want a 4 inch wide transition strip. It's really simple for most of them, drill into foundation with masonry bits, install channel onto foundation with screws and snap the strip into the channel. How wide is the opening? Also, you might have to trim up the baseboard with a oscillating tool.

Somethign like this...

4" strip of deelux linoleum from a dumpster dive should do the trick.

What? No JB weld handy?

I don’t think a JB Weld handy is a good idea.

I think I’m going to fox the walls and ceiling first and think about it. I’m leaning towards the stained wood transition

Isn’t it the same tile on both sides of the gap?

Why does the last 3% of a project take 97 % of the effort

Burn it down and do an insurance claim, it will never look right...

Maybe you’re right, I thought this was wood glue between wood planks. Would be a much easier fix if it was an engineered wood, guess I should have read it closer and not just looked at the pic.