DnD 5e Spells – Twinned Glyph of Warding and Storing Different Spells

It does take two spell slots.

The first line of the spell describes what happens when you cast the Glyph of Warding:

When you cast this spell, you inscribe a glyph that harms other creatures...

Later, it specifies that if you choose the spell glyph option, you cast the spell you choose to store (emphasis added):

You can store a prepared spell of 3rd level or lower in the glyph by casting it as part of creating the glyph.

PHB 201 specifies that when the "casting" wording is used, it uses up a spell slot:

When a character casts a spell, he or she expends a slot of that spell’s level or higher, effectively “filling” a slot with the spell.

This interpretation is consistent with other game mechanics that are more explicit about how this works. For example, contingency works this way:

You cast that spell, called the contingent spell, as part of casting contingency, expending Spell Slots for both, but the contingent spell doesn't come into effect.

or the ring of spell storing:

Any creature can Cast a Spell of 1st through 5th level into the ring by touching the ring as the spell is cast. The spell has no effect, other than to be stored in the ring.

Two slots -- one for the stored spell, and one for the Glyph (which must be the same level slot (or higher) as the spell being stored).

The Spell Glyph option of the Glyph of Warding spell (PHB, p. 246-247) states:

You can store a prepared spell of 3rd level or lower in the glyph by casting it as part of creating the glyph. [...] The spell being stored has no immediate effect when cast in this way. When the glyph is triggered, the stored spell is cast. [...]

Both slots are expended when the Glyph with the stored spell is created, as that is when the spell caster is casting both spells.

There's nothing in the spell description that says it allows an extra spell to be cast and stored without using a spell slot. Using a spell slot is how casting and storing spells both normally work (per p. 201 of the PHB), so that's the general rule, and it holds unless a specific rule says otherwise for a particular application - which in this case it does not.