I make this 18.5725. I think you've multiplied the extra burst damage dice twice - there are 2d10 added (average 11), which should be multiplied by the chance of a critical (0.1).
i.e. the term (11[0.1(3-1)]) should be (5.5[0.1(3-1)]) or (11[0.1]).
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As regards the utility of the burst weapons as a whole, I don't think they're worth it in the general case. I think perhaps a doubling of the extra damage dice might be called for.
That said, they have a far higher utility when used against a creature with some (fairly low) energy resistances. Basically, the longsowrd +1 with flaming and shocking gains no benefit against a creature with Fire Resitance 10 and Electricity Resistance 10, while the longsword +1 of flaming burst might. Although even there, the benefit is negligible - average fire damage on the crit is still not enough to get through.