There are a number of studies that have examined the life cycle energy costs for photovoltaic panels.
Start with this and go from there. Some numbers I've seen (like
this) indicate the energy payback for monocrystalline PV modules is around two years; less for other technologies. Those numbers are from 2011, so I suspect that with increased manufacturing volume the numbers are even more favorable today.
A different argument that could be made comes down to basic economics. If solar panels took substantially more energy to manufacture than they produce over their lifespan, it would be reflected in their price. As the GP argued, albeit poorly, one can look at the price for a commodity and get from it a rough sense of the energy investment that it embodies. The wholesale price of PV modules is $1-2 per W of capacity, which one could argue represents tens of kWh of energy input. Even if there are externalities not captured in the price, and the total energy cost was hundreds of kWh per panel, that's still one or two orders of magnitude lower than the total lifetime output of the same panel.