Randy,
The BLUE BOOK OF GUN VALUES lists a value of around $2500 for a low condition GH Parker. Values are hard without the gun in hand but as a collector of 10 gauge Parkers I would not offer $2500 for this E grade. The "E" on the watertable is the grade. E was used for 10 gauge Grade 2 Parkers. Later G replaced the E's.
For a value comparison, please look at this GHE 12 that has been up for auction/sale for a couple months.
http://www.gunbroker.com/Auction/Vie...Item=278192456
This is what appears to be a fairly high condition Grade 2 ejector gun in 12 gauge for $1900. I've bought from the seller and while he doesn't give away guns, his prices are reasonable. 12 gauges are easier to sell than 10 gauges. Ejector guns command a higher price by 25-50% than extractor guns. The wood on this gun is in good condition. The Damascus pattern is visible and if original, very visible. The "D" on your barrel flat is for Damascus.
On the subject EH (H is for the Hammerless Action) the head of the stock is split. A repair will be about $200, maybe less. There may be a split on the right side of the stock from the butt to the grip. A positive factor is that the buttstock has a lot of figure in it.
The barrels look to have flecking over their entirety. I hope the bores are not the same. If the bores are like mirrors and haven't been honed to achieve their present smoothness that would be another plus. Do the barrels still have at least .030" constrictions (chokes)?
So, how much would it bring? Maybe $1000 but probably $800. The gun does have a lot of potential. Have the Damascus pattern redone for $400, Repair, refinish, and rechecker the wood, $500 (higher or lower), and install a new pad ($100 for the correct to the period pad) and for a $1000 investment you will have a gun that looks great. Unfortunately it will be a few years before a gun such as that will fetch around $2000. The gun market is showing signs of rising in values just as is the stock market... I have several E grades in good original condition which I’d be hard pressed to receive $2000 for today.
Or, you could repair the stock yourself if you can read and follow directions and are a decent gunsmith, and replace the pad and have a nice "shooter". Just repairing the stock and a careful light cleaning of the gun’s exterior will bring the gun into a shooting or selling condition.
PS: The #3 frame size is the most common for Parker 10 gauges. If it were a #2 or #4 then it would be a little rare and be of higher value to some collectors.
I hope this helps,
Mark