As far I understand correctly, the objective is to find a nonce which creates a hash with the specified difficulty. The current difficulty being around 1.4 trillion. If that is so, why doesn't a machine which runs at 14 TH/s calculate the nonce in under a second?
As explained here in the Bitcoin Wiki, the formula for using the Difficulty to determine the expected time to solve a block is:
time = difficulty * 2**32 / hashrate
Currently, the difficulty is 1,452,839,779,146 so a 14TH/s ASIC miner would be expected to, on average, solve a block with
time = 1,452,839,779,146 * 4,294,967,296 / 14,000,000,000,000
which gives a result of 445707095 seconds, which is about 14 yrs, if I've done my calculations correctly.
To double check that the technique works:
Using the current approx network hashrate (according to blockchain.info) of 10,183,000TH/s, and the same difficulty as indicated above, the formula gives a result of 612s to solve a block, which is the expected result of approx 10 mins.