You wrote:

Both left hand and right hand side of second expression is the sum of eight quantities

So I guessed your Mathematica expression is wrong. You forgot a Plus sign here

So, after correcting:

Solve[.... == ... .. && ... + ... == ... + ...] // N

{{h1 -> 0.00998752, h2 -> 0.017552}, {h1 -> 0.00998752, h2 -> 5.94171}}

The aimless debugger strikes again.