I have an EEE PC with an additional charger which I can use inside my car. It plugs into the cigarette lighter thingie that seems to be standard in every car. When on the move, it does allow me to charge my laptop that way. Very practical.
But charging through an USB port is only possible at one side of the USB connection, not on both sides. Basically, the USB ports on a laptop are used to send a signal out, thus they can be used to power up something. Many rechargable USB devices are designed to get a signal in, thus they are waiting until they receive power through the port. Technically, this is all just a one-direction street.
Still, they could make a laptop that can be recharged through the USB port, if they add a receiving end to it. Basically, that would mean that you can't connect a device to your laptop, but you would be connecting your laptop, as if it's just another device, to another PC. Would this be practical? Maybe if you want to do this to set up a special network or whatever but no one has seen some true value in such a setup. Basically, you'd be downgrading your laptop to a portable hard disk.
Still, as mentioned by the others, an average laptop will require a bit more power to fully charge than other devices. Especially the big screen and the disks are big energy consumers, although the CPU itself also puts some strain on the system. The power a device receives through the USB port is just a fraction of the power that a device would receive through a direct power connection.
The closest thing to a computer that can be recharged through an USB port would be a Smartphone with Windows Mobile. Or perhaps an UMPC system, but I don't know any good UMPC that is recharged this way. I assume you also have a few wishes concerning operating system, diskspace and memory.
Best Answer
The S10 charger is probably limited to 9V and 1.7amps of current, probably putting out 15 watts of power. It might even be able to give 25 watts. (A little above 2.5 amps). It is intended to charge a phone with a small 3.7V battery.
Your laptop probably expects either 12V, 15V, or 20V in order to charge. It has a much larger set of batteries to charge and requires a higher voltage in order to drive current into the battery cells.
USB C Power Delivery may mean we now have a single connector and cable to charge things but it does mean we also need chargers capable of meeting the demands of the devices attached. A laptop USB C charger may well be able to put out up to 100watts of power (20v at 5A) while a phone charger has almost no need to supply that much.
USB PD chargers can be selective about what voltages and currents they support. This can save a lot of expensive components for devices intended to only charge phones.
Mobile phone charger: 5V, 9V, 10V (Samsung)
Laptop USB C charger: 5V, 9V, 12V, 15V, 20V
USB PD starts a connection at the standard 5V (to allow basic electronics to work) and then allows the two devices to negotiate supported voltages, if neither device supports a common required voltage level then they will simply stay at 5V. For a phone that may mean slow charging, for a laptop it will mean no charging.
If a laptop battery has multiple cells then it may well operate at 7.2V or 14.4V, the voltage from your charger needs to be higher than that voltage. Hence many high powered laptops need either a 15V or 20V charger. Otherwise the laptop needs extra charging circuitry to "boost" the voltage up to a good level and draw more current to compensate. That is extra cost and most manufacturers will simply say "use the manufacturer supplied charger" which puts out the correct voltage and leave it at that.
Even if you have a 7.2V battery a 9V charger may only be able to put out 1.5-2A of current. Depending on the size of the battery this may result in a charging time that is excessive of the order or 4 or more hours. Increasing the current will result in more heat generated in wires and could be a hazard. Increased voltage on the other hand (20V instead of 9V) would reduce heat at the wiring and connectors at the cost of a slight increase in conversion loss inside the device which would be handled by the cooling there.
While you should be able to charge your phone using a laptop charger, even if slowly at 5V, you won't be able to charge your laptop using a phone charger.
There are many hits on Google that suggest that USB charging will work on your device.