Is the word e-mail the same in Brazilian and European Portuguese?

Yes

The word "e-mail" (and its variant "email") is identical in meaning, grammar, and spelling across both Brazilian and Continental Portuguese. In both varieties, it is a masculine noun (o e-mail). The only significant difference is pronunciation. In Brazil, the initial "e" is often pronounced with a more open sound or even as an "i" (sounding like ee-mê-il), whereas in Portugal, the "e" is typically pronounced as a much shorter, closed vowel (/e/).

Brazilian Portuguese Examples

1. Eu te mando o e-mail agora. (I'll send you the email now.)
2. Você recebeu o e-mail que eu te enviei? (Did you receive the email I sent you?)
3. Preciso checar meu e-mail no trabalho. (I need to check my email at work.)
4. O e-mail caiu direto na caixa de spam. (The email went straight to the spam folder.)
5. Me manda um e-mail quando puder. (Send me an email when you can.)

Portuguese (Portugal) Examples

1. Eu envio-te o e-mail agora. (I'll send you the email now.)
2. Recebeste o e-mail que te enviei? (Did you receive the email I sent you?)
3. Preciso de ver o meu e-mail no trabalho. (I need to check my email at work.)
4. O e-mail caiu diretamente na pasta de spam. (The email went directly to the spam folder.)
5. Envia-me um e-mail quando puderes. (Send me an email when you can.)