without external source
You can't. The Arduino Uno has no real-time clock. A real-time clock is only something like $1 from eBay. For example the DS1307 or DS3231. I found 5 x boards pre-assembled with the clock chip, including battery holder, crystal, chip, and circuit board for $US 4.20 on eBay. Batteries not supplied.
Hook that up to the I2C pins (A4 and A5), set the time once using a suitable sketch, and then you are ready to roll.
If you just want to do something every 24 hours (not necessarily at 9:36 a.m.) then you can just use
millis to find when the appropriate number of milliseconds has elapsed. The result from
millis will wrap every 49 days roughly but you don't have to worry about that.
Note that this won't let you log the date and time, but you can log something (eg. the temperature) every day, you would just have to know when you started logging.