The 10 gallon is fine for a while...corns like to hide a lot, so they don't need that much room...I had Snakey (my Corn) in a 40 gallon tank and he just chilled under his hide box all day...the hide box took up about as much space as a 5 gallon tank...and Snakey's 3 years old.
You'll know your snake is shedding, because his eyes will turn blueish gray and his skin will look dull. Don't bother trying to feed him now...in a few days, his eyes will return to normal and a few days after that, he will shed. After he sheds, carefully check for any leftover skin on his body...especially the eyes! There could be eyecaps left behind on his eyes. If there is leftover skin, you can soak him in warm water or wet a pillowcase with warm water and put him in there...he'll move against the pillowcase and the skin should come off. JUST MAKE SURE HE CAN BREATHE!
Your snake won't be able to see much when his eyes are blue-gray...so he may be startled if you handle him...you may want to leave him alone, because the shedding phase is not the most comfortable for your snake...however, he'll be fine! 
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1.0 Corn Snake (Snakey)
0.0.1 Ball Python (Sosa)
0.0.1 Pine Snake (no name yet)