The tablet is not in the instance, it is just outside the instance.

Enter the Uldaman caves as though you are heading toward the instance. Keep following the path, you should run off a small ledge and through a tunnel. Continue following the path until you get to a much higher ledge overlooking the instance entrance. Don't jump off the ledge! Ignore the instance entrance, keep following the path round to the left, almost immediately you will come to a kind of fork, keep to the left. You will shortly come across an entrance on your right to a room full of troggs, ignore this room, stay left, keep going. Next on your right you should see a big corded off room that is set slightly lower than the path and is full of dwarves, this is the room! (if you accidentally miss this and go too far don't worry you will get to a dead end almost straight away) The room is full of various Elites who will aggro each other easily, so if you plan to solo this then plan to fight 2-4 Elites at once :) The tablet is inside that big chest (ark-like thing) in the middle of the room.

I soloed this with a lvl44 mage, I died in the main room but I ressed just behind the chest without aggroing anything, grabbed the tablet and teleported outta there! Good luck!

Here's how I'd describe finding it:

You enter Uldaman (main entrance). You make your way toward where you can first see the instance (you're up on a high path and you have the choice there of just simply dropping down to the lower area and running into the instance -- pretty much everyone I see does that).

Now, you don't drop down, you follow the path you're on and then you come to a fork really soon. Keep right and you go to the room where the instance is. Go left instead. There are dwarves here, so fight them. Then there are a few choices. The room on the most right of this (which looks most like a room on the minimap because it's a different color than the mined out areas) is guarded by Troggs. That's for Reclaimed Treasure, not for this quest. The room to the left of that, which is a mined-out room so not a different color on your mini-map, is the room you want. More dwarves, kill kill kill, and presto you see what that picture up above shows. Tadaa.

ok wow!&nbsp what a mess of info lets get some good stuff up here to help people out already.

here are links to screenshots and the info to go with, pardon the arrow directions on minimap and times on the screenshots as i took the screenshots on the way out after i was already done.

ok here we are at the uld ent as ya enter badlands from loch moden its just in and to the right a bit.
http://i2.photobucket.com/albums/y17/sornlia/uld1.jpg

i found my locs didnt change or update as i was inside so locs werent helping what so ever, so here is pics of the area and our position on mini map is shown.&nbsp you want to jump down and go in that tunnel im looking at here.
http://i2.photobucket.com/albums/y17/sornlia/uld2.jpg

when you reach the corner and see hammertoe ya know youre in the right area. /wave hammertoe
http://i2.photobucket.com/albums/y17/sornlia/uld3.jpg

keep on goin in, you will see the instance entrance that most people jump down from the ledge too... dont jump down!&nbsp its not inside, its out in dig one.
http://i2.photobucket.com/albums/y17/sornlia/uld4.jpg

scoot on down clear your way, first right youll see the trogg stonevault guys, ignore them!&nbsp ya dont need to kill em or head that way, clear on up the hall. *see position on minimap*
http://i2.photobucket.com/albums/y17/sornlia/uld5.jpg

its the first right past the stonevault one, in the sealed hall. tadaaa! clear up around and all the big baddies, open the chest and get your tablet of ryun'eh!
http://i2.photobucket.com/albums/y17/sornlia/uld6.jpg

if nothing else ~ i hope you can follow the minimap on these linked screenshots and get yourself there!&nbsp gluck and safe ventures.

~ edit edit edit .. holy typos *blush*

Leads to "To Ironforge for Yagyin's Digest" quest (https://classicdb.ch/?quest=727)

Theldurin has for foreseen a doom coming. He wants you to get the Tablet of Ryun'eh for him. It can be found in the center of the Sealed Hall in southern area before the instance portal.

Isn't this chest in the same room with the lost dwarves?

This tablet is now much easier to get for anyone over the level of 34-35. The mobs outside of Uldaman are no longer elite, just be prepared for multiple mobs on some pulls :).

Actually it's inside the front entrance to Uldaman (not the instance, but the area where the Dwarves are guarding). It's south of the main chamber, next to the Northern Dining Hall. You'll see a large "Ancient Chest" which is clickable in the center of the room.

If you use the coords given by Atrapost you'll find yourself in the middle of the desert with no chest in sight.