If it changes state every 10 seconds, as stated, the update() function will update the EEPROM as Duncan has stated. This is a very example to present for the use of the EEPROM.

One way you could use them to store a richer configuration that protects against EEPROM that exceeded its write count by storing a structure with a flag pointing to the valid and confirmed data.

Or simpler, you could store the EEPROM address of the valid data in EEPROM, and update to a different address if it ever fails to update & check properly. E.g: stateAddress=EEPROM.Read(EEPROM.end()); ledState=EEPROM.Read(stateAddress);

Jet, could you guide me, to write what you explain, I am a novice user, if you want I will send you my email, thank you, in advance!
mario172 at msn.com

It doesn’t work that way . At around 100,000 cycles the memory you have used will stop functioning So if you change Address 0 100,000 times it will stop changing . but address 1 should still change,

It is what it is. alternative would be a replaceable external EEPROM

That would at least double the life of the eeprom.

set all eeprom to FF then you save at address = address +1 . When you reset the program looks for the first FF then sets the address 1 less and reads the Led. Then after next button press save at address = address +1. With a Nano you now get 11000+ days – around 30 + years.