Third-country nationals require a national visa when they are going to stay in Spain for more than 90 days (in any 180-day period) for the purposes of work, study or establishing their residence. They also need a national visa when moving to Spain to work for a period of under 90 days.
Citizens of the European Union or of the States of the European Economic Area or Switzerland do not need a visa to establish their residence in Spain or for long-term studies or to work. However, once in Spain, they must be entered on the Register for Citizens of the Union. Family members accompanying them, and who benefit from the right to free movement, must apply for a residence permit in Spain. If they need a stay visa because of their nationality, they must obtain a visa for family members of a citizen of the Union (see section "Visas for family members of a citizen of the Union​").
The national visa allows the holder to travel to Spain and to transit through and move around the territory of any Schengen State for a maximum of 90 days. However, it does not automatically entitle them to enter the Schengen area. The border authorities can refuse entry if not all entry requirements are met (See section "Conditions for entry into Spain").

More Spanish Visa information, please check here: https://www.exteriores.gob.es/Embajadas/seul/en/ServiciosConsulares/Paginas/Consular/Visados-nacionales-Informacion-general.aspx

ICAME letter of Invitation

A Letter of Invitation is a proof that your paper submission and registration application are accepted by the conference committees board. It perhaps could help with your visa application. However, it does not guarantee you a visa.