Write an email stating the facts and apologizing for your mistake. Just admit and inform that you will see that you will not repeat and follow the policies of the company in toto. Do not put in too many words which might be confusing. Accept your folly and move on. Try to send only to the concerned person, do not involve any other person.
Thanks and Regards
17th January 2019 From India, Hyderabad
Are you back on duty after this leave. What was the response your HoD about your 'unauthorised leave'.
First of all let me know what you mean by saying 'unauthorised leave' ? do you mean to say either i) applied for leave but 'not approved' or ii) didn't go to work simply without any intimation to your HoD or time office? or iii) don't have leave balance, hence could not seek approved leave or iv) any other reason. All these might result in 'Loss of pay' and/or 'absent'. And you didn't mention how many days you availed like this. Is it for the first time like this? If it is for the first time there is a chance of extracting a pardon.
Whatever the reason could be, the long and short of the story is 'you did not attend to duty as there was no approved leave'.
The fact is you cannot undone the mistake and therefore reconcile to the situation warrants.
So, I suggest you to meet your HoD or reporting officer or any other authorised person who is supposed to sanction your leave.DON'T WAIT TILL THEY CALL YOU. YOU GO FIRST AND MEET THEM. Explain the circumstances, orally, as to why you could not obtain prior approval and the urgency involved forcing you to abstain from work on these days of your absence and apologize for your mistake. If they pardon you on this, well and good. If they further insist for a written letter of apology, write it and give then and there and might solve your problem. Don't worry, you created the problem, you only can solve it.
18th January 2019 From India, Bangalore