I don’t think there is an option to do that. You can edit the theme to remove those elements, but then you will have a problem when the theme gets updated (pretty frequently for Twenty Ten right now.
But if you did want to do it, you have three ways to do it:
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You can edit PHP files for the presentation (e.g. loop.php) under Appearance/Editor and delete the whole section responsible for it
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You can edit functions.php that contains twentyten_posted_on and twentyten_posted_in functions to stub them out to return nothing
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You can edit CSS to make corresponding classes (entry-meta and entry-utility I believe) to be invisible. WordPress still has to do all work and it is still there in source code, but it could be the faster option. You could even use FireBug to test whether the display will look correct when you remove those.
There are better and more esoteric ways to do it (child themes), but I am not sure I could describe it in a text box.