I'm assuming you're in North America, which means you're on a center tapped supply.
There's a transformer on top of a pole near your house which drops the voltage from the transmission voltage to the household voltage of 240 V.
BUT! They grab one leg from the top of the transformer, and the other from the bottom, and ground in the middle. This means your house is supplied with two legs, each of 120 V.
Those two lines at the top are two separate 120 V legs, EACH rated for up to 100 A.
Half of your circuits are on one leg, and the other half are on the other. What this means, if we don't have any 240 V breakers, is you effectively have two separate supplies of 120 V, up to 100 A. In a pure 120 V world, your 100 A supply is effectively a 200 A supply. (Caution with this metaphor - it's not accurate, but helps understanding).
On your panel, typically, the even numbered circuits are on one leg, and the odd numbers on the other.
This means you can put in a double wide breaker, which spans two slots, and get 240 volts by bridging the two legs.
The tandems split one slot effectively into two, but both are on the same leg.
So, to add up your currents, you need to add up the odd numbered currents, and the even numbered currents separately. BUT the 240s get added to both.
I did a quick guess as to how your panel is configured, and got 81.1 A and 67.4 A. Which is close.
Some 240 W appliances are not pure 240 W. For example, the dryer may have a 240 V heating element, but only a 120 V motor, bridging only one leg of the 240 V circuit This imbalance could be an explanation for the discrepancy on the one leg.
Quick and dirty - The current sum of all circuits should be close to the current sum of the two supply legs. In the case of the 240 V breakers, you'll need to add them in twice, because they affect both legs. I get 148.5 A for the breakers and 144.5 A for the supply, which is close enough given leg imbalances and measurement issues.