D10 (10-sided dice) statistics/probability question

I am designing a game and am trying to determine the advantage of a system I'm considering using for dice rolls.

Two players each roll two D10s (a D10 is a 10-sided die with the numbers 0-9 engraved one on each face)
Player One reads the total of the two dice by taking the HIGH number first. So if he rolled a 7 and a 2 his result is 72
Player Two reads the total of the two dice by taking the LOW number first. If he rolled a 7 and a 2 his result would be 27

What is the % advantage that player one gains under these rules. In other words, if two players roll against one another under these rules, how many times would player one be expected to have the higher roll out of every 100 plays?

I don't have the math to figure this out, so if one of you folks don't help me out I'll have to resort to rolling a whole bunch of dice to get a rough answer by trial and error.

Thanks for any help!

Is this a game that you are designing for use in a casino or a board game concept for consumer use at home?

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silly

A board game. Definitely NOT for casino use! Although, as much fun as folks get rolling unusual dice, maybe someone should come up with a casino game using d8s, d10s, d12s, d20s etc.

My gut feeling was that there should be around a 74% to 26% (if I give ties to Player 2) advantage for the player who reads high die first which is exactly what your example using d6s shows (although there can be ties if both players roll the same set of doubles, right?). So maybe this is one of the times where the answer is straightforward.

The barrier to getting d8, d10, d12, etc. dice games in a casino is the fact that any of these cannot as of yet be made as "Legal Dice". Since the d12 is a platonic solid, there is a chance.
Basically, "Legal Dice" must be equal-weighted on all sides (uniform density), and the measurements on any face (the area) must be .01% or less. d12 Dice are made using vertex injection, that fouls said vertex. Face injection has molding problems and spur problems, but the face could be levelled and rendered dimensionally acceptable.

Right now there are several types of d(x) dice with minimal polishing suitable for accurate game-play, but they just don;t cut the mustard "Legally"

ties are possible if both players roll the same pairs of numbers.