Escribo el número de cuenta.

In Spanish, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• Escribo = I write / I am writing
• The -o ending tells you it is yo

So Escribo el número de cuenta is completely natural.
You could say Yo escribo el número de cuenta, but that usually adds emphasis, contrast, or clarity.

Escribo is the present indicative, first person singular, of escribir.

Depending on context, it can mean:

• I write
• I am writing

Spanish often uses the simple present in places where English might use either the simple present or the present progressive.

Escribir is a regular -ir verb in the present tense.

For yo forms, you:

1. remove -ir
2. add -o

So:

• escribir → escrib-
  • o → escribo

This is the normal pattern for regular -ir verbs in the yo form.

Spanish does not always need a separate word for down in this kind of sentence.
The verb escribir can often cover the idea of write or write down, depending on context.

So Escribo el número de cuenta can naturally express the idea of writing it down.

That said, in some contexts a native speaker might also use anotar:

• Anoto el número de cuenta

That often feels closer to I write down / note down the account number.

Because número is a masculine noun in Spanish.

So it takes:

• el número = the number

Even though learners sometimes rely on word endings, what matters is the noun’s grammatical gender.
In this case, número is masculine, so el is correct.

The accent mark in número is required.

Spanish stress rules say that words stressed on the third-to-last syllable always need a written accent.
Nú-me-ro is stressed on the first syllable, so it must be written número.

Without the accent, the word would not follow normal spelling rules.

Número de cuenta is a standard noun phrase meaning account number.

Here, de cuenta works like a description of what kind of number it is. In Spanish, when one noun classifies another, the article is often omitted after de.

So:

• número de cuenta = account number

If you said número de la cuenta, it would sound more like the number of the account/bill, which is a different idea and is not the usual banking expression.

Because el número de cuenta is a direct object, and it refers to a thing, not a person.

In Spanish, the personal a is usually used before specific people:

• Veo a María

But with things, you normally do not use a:

• Escribo el número de cuenta

So the sentence is correct without a.

It can mean either one, depending on context.

Escribo el número de cuenta can mean:

• I write the account number / I usually write the account number
• I am writing the account number

Spanish present tense is flexible in this way.
If the speaker wants to make the ongoing action extra explicit, they could also say:

• Estoy escribiendo el número de cuenta

But the original sentence is still perfectly normal.