Here is the solution:

Take any ten pennies and turn them over.
They are group number one.   The rest of the pennies are group number two.

If you don't believe that this works, try it!

Here is a table showing the possible coins that you could select for group one, and the resulting number of tails in group two:

Group One (10 coins) If you select:		Group Two (90 coins)
0 Tails	10 Heads	10 Tails
1 Tail	9 Heads	9 Tails
2 Tails	8 Heads	8 Tails
3 Tails	7 Heads	7 Tails
4 Tails	6 Heads	6 Tails
5 Tails	5 Heads	5 Tails
6 Tails	4 Heads	4 Tails
7 Tails	3 Heads	3 Tails
8 Tails	2 Heads	2 Tails
9 Tails	1 Heads	1 Tail
10 Tails	0 Heads	0 Tails