The trick is a variant of Affinities on pp. 131-133 in Volume II of The Vernon Chronicles, about which Minch wrote "The mathematical principle underlying this effect is an aged one."
The procedures used in Affinities appear a little more clear-cut, and of course have a Vernon touch or two. It was mentioned that the trick becomes more perplexing upon being repeated several times. (But you'd better "pick your audience" for this wisely!)
Affinities goes to a count of 13, not 10, and uses 10 as the number you add to the values of the two upturned cards. If you try the experiment of starting the count of each packet with an ace (as I did years ago when trying to understand why it worked), I believe you'll quickly see why it works as it does. Just realize what the difference will be when one of the upturned packets has a two instead of an ace, then a three, etc...
I hope this is of help.