Tjónsnúmerið er í bréfinu.

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word like the.

• tjónsnúmer = claim number / damage number
• tjónsnúmerið = the claim number

The ending -ið is the neuter singular definite article here.

It is a compound noun:

• tjón = damage, loss, claim-related damage
• númer = number
• tjónsnúmer = claim number / damage reference number

Then the definite article is added:

• tjónsnúmerið = the claim number

Compound nouns are extremely common in Icelandic, just as in English.

There are two things happening here:

1. í is a preposition meaning in
2. After í, Icelandic uses different cases depending on meaning

Here the meaning is location: in the letter, not motion into the letter.
So í takes the dative case.

• base noun: bréf = letter
• definite form in dative singular: bréfinu = in the letter / the letter, in dative form

So:

• í bréfinu = in the letter

Í can take either the accusative or the dative.

• dative = location, being somewhere
  
  • í bréfinu = in the letter
• accusative = movement into something
  
  • for example, setja í bréfið = put into the letter

In your sentence, the claim number is located in the letter, so the dative is used.

Er is the 3rd person singular present tense of vera, which means to be.

So here it means is:

• Tjónsnúmerið er í bréfinu.
• The claim number is in the letter.

Some useful forms of vera in the present tense are:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

This is the normal Icelandic sentence pattern for a simple statement:

• subject
  • verb
    • other information

So:

• Tjónsnúmerið = subject
• er = verb
• í bréfinu = prepositional phrase

That gives the standard meaning: The claim number is in the letter.

Icelandic word order can change for emphasis, but this version is the most neutral and natural.

Both are neuter nouns.

You can see that in their definite forms:

• tjónsnúmerið uses the neuter definite ending -ið
• bréfinu is the neuter dative singular definite form

Knowing the gender helps you choose the correct article endings and adjective forms later.

You would remove the attached definite article from both nouns:

• Tjónsnúmer er í bréfi.

However, that sounds less natural in many real contexts, because English and Icelandic often prefer the definite form when referring to a specific item already understood in the situation.

More commonly:

• Tjónsnúmerið er í bréfinu. = the claim number is in the letter

It comes from the noun bréf.

Step by step:

• bréf = letter
• definite singular nominative/accusative: bréfið = the letter
• dative singular definite: bréfinu = to/in/from the letter, depending on the preposition

In this sentence, í requires the dative for location, so you get í bréfinu.

A rough pronunciation guide for an English speaker could be:

• Tjónsnúmerið ≈ tyohns-noo-meh-rith
• er ≈ ehr
• í ≈ ee
• bréfinu ≈ breh-fi-nu

A few important notes:

• tj in tjón sounds like a ty-type sound
• ú is a long oo
• ð in -ið is like a soft th in this
• é sounds like ye or a clear long eh/ye sound depending on accent and speech

The exact pronunciation varies a bit, but that should get you close.

Not usually in a careful translation, because tjónsnúmer is more specific than just number. It refers to a claim, loss, or damage case number.

So claim number or damage claim number is better than simply number.

That said, in a real insurance or claims context, English speakers might shorten it in conversation if the context is obvious.