Both Eagleye and Leftlane make a couple good points but they might not apply to your situation entirely.
You haven't said what the pitch is going to be on this roof nor how much snow you have on the level at one time. From what I can find, Indiana rarely has more than 10 inches remaining at any one time. I assume that is pretty wet.
But a cubic foot of solid ice weighs 57 pounds so I think you'd be safe calculating half of that or less for your load.
The US legal span for rafters in snow regions with a dead load of 20 PSF allows a horizontal span of 9'9" for 2x6 on 24" centers using #2 material. Greater than that, depending on the slope. Example: if your slope is 4/12 , you multiply by a conversion factor of 1.054 and you come up with a span of 123.318"
Personally, I wouldn't feel comfortable going that far. Nevertheless, the roof you describe is exactly the size of the roof over my deck. 8x36. Mine has a 4/12 pitch and 2x6 on 24's for rafters. Nailers with metal on top. No plywood. All that does is add weight. Currently I have 60 inches of snow on that roof. Without a doubt it is not as dense as the snow you likely get, but I probably have 5 times as much as you will have at one time.
I agree with Leftlane when he says you don't want to just screw a ledgerboard up there. BUT....you can do that just to hold it in place while you do things right. Once that ledgerboard is where you want it...drill through it and into the studs of the existing exterior wall. Next run a 3/8"x 5" galvanized lag into the existing studs. Do it every 4 feet. That won't fail on you unless there is a tornado.
I also agree that you must use the proper flashing where the new roof meets the existing building. You could even run some caulk on the backside of the flashing if you wanted.
Lots of ways to do things but it's always best to do it the best possible way the first time. It might cost a bit more but not as much as re-doing it !!
I am going to insist that you NOT use two 2x10's for your header that carries the rafter tails. Two 2x10's measure 3 inches thick. The 4x4 post you are setting that on measure 3.5 inches thick. That half inch difference is just enough to allow for movement. It is imperative that everything be plumb and stable if you expect to support a load. Posts and header need to be plumb in all directions.
So.........do it right. Buy two 4x10x18' beams, and the correct Simpson hardware to hold it where it is supposed to be. All the pieces are engineered to fit. Be sure to include some diagonals to eliminate sway.
One more thing PLEASE do not set your uprights on the deck surface. Run them through the decking and support them on concrete. Either adjustable piers or just a poured concrete pad about 10"x10"x10". You need to transfer that roof load to the ground. Not the deck. Be sure to use pressure treated material in contact with the ground or concrete
I'm including some pix of mine that has withstood the test of time, snow, and earthquakes. Mine has a hip roof so that may be different from yours as it wraps around three sides
This is how you need to join your headers
Use plenty of Simpson connectors.Don't scrimp on doing it right