Please go to "eTax Portal, Ministry of Finance" to apply online for E-Invoice Alphanumeric Numbers. Basically, it takes 7 days for local branch or office of National Taxation Bureau to review and approve.
-Path: eTax Portal, Ministry of Finance /Tax on Cross-border Electronic commerce/Cloud Invoice/Apply for Alphanumeric Letters online"【https://www.etax.nat.gov.tw/etwmain/en/etw310w/cases/services/olfetwb36/apply】
-Instructions for Cross-Border Electronic Commerce Business Entity to Apply for Electronic Invoice Letter Track Number【Chinese Ver.】【English Ver.】